Geometry & Mensuration MCQs With Answers
Shapes, angles and formulas turn up in almost every mathematics paper. These geometry and mensuration MCQs test triangle and polygon angle sums, types of triangles, the Pythagoras theorem, diagonals of squares and rectangles, area and perimeter of rectangles, triangles, circles, rhombuses and trapeziums, sectors and semicircles, and the volume and surface area of cubes, cylinders, cones, spheres and hemispheres, along with how area and volume change when a side or radius is scaled. They are ideal for PPSC, FPSC, NTS and teaching tests.
Take a scored quiz instead →A triangle has angles 60 and 70 degrees. What is the third angle?
• The sum of angles in a triangle is 180 degrees.
• 180 - (60 + 70) = 180 - 130 = 50.
A square has a side of 4 cm. What is its area?
• Area of a square = side * side = 4 * 4 = 16.
The perimeter of a rectangle with length 5 and width 3 is:
• Perimeter = 2 * (length + width) = 2 * (5 + 3) = 2 * 8 = 16.
What is the sum of the interior angles of a pentagon?
Sum of interior angles of an n-sided polygon = (n − 2) × 180°.
For a pentagon, n = 5: 3 × 180° = 540°.
Each interior angle of a regular polygon is 140°. How many sides does it have?
Each exterior angle = 180° − 140° = 40°, and the exterior angles of any polygon add up to 360°.
Number of sides = 360° ÷ 40° = 9.
If a triangle has all sides equal, it is called:
• Equilateral means all sides are equal.
The sum of angles in a triangle is:
Fact: Interior angles of a triangle always sum to 180°.
A rectangular field has length 20m and width 10m. What is its perimeter?
2 * (20 + 10) = 60.
A cube has how many edges?
A cube has 12 edges.
What is the size of each interior angle of a regular hexagon?
Sum of interior angles = (6 − 2) × 180° = 720°.
Each angle = 720° ÷ 6 = 120°.
Area of a triangle with base 6cm and height 4cm?
0.5 * 6 * 4 = 12.
Sides in a heptagon?
Heptagon has 7 sides.
What is the perimeter of a rectangle with length 10cm and width 5cm?
2 * (10 + 5) = 30.
A square has a side of 6cm. What is its area?
6 * 6 = 36.
If a triangle has two equal sides, it is:
Definition.
Through what angle does the minute hand of a clock turn in 25 minutes?
The minute hand turns 360° in 60 minutes, that is 6° per minute.
In 25 minutes it turns 25 × 6° = 150°.
A cube has how many faces?
Fact.
A rectangle has sides 7m and 2m. Area?
7 * 2 = 14.
If a triangle has a base of 10cm and an area of 50cm², its height is:
Area = 0.5 * b * h => 50 = 5 * h => h = 10.
How many faces has a triangular prism?
2 triangular + 3 rectangular = 5.
A rectangle has length 6m and width 4m. Perimeter is:
2*(6+4) = 20.
How many diagonals does a hexagon have?
Number of diagonals of an n-sided polygon = n(n − 3)/2.
For a hexagon, n = 6: 6 × 3 ÷ 2 = 9.
A triangle in which all three angles are 60° is called:
If all three angles are equal (60° each), all three sides are also equal, so the triangle is equilateral. A scalene triangle has all sides different, an obtuse triangle has one angle above 90° and a right triangle has one angle of 90°.
A rectangle has sides 5m and 4m. Area?
5*4=20.
Number of sides in a decagon?
10 sides.
Two angles of a triangle are 47° and 68°. What is the third angle?
The angles of a triangle add up to 180°.
Third angle = 180° − (47° + 68°) = 65°.
If the area of a square is 144 cm², what is its perimeter?
Side = sqrt(144) = 12. Perimeter = 4 * 12 = 48.
A rectangle has width 5cm, diagonal 13cm. Length is:
sqrt(13^2 - 5^2) = sqrt(169-25) = 12.
Volume of a cube with side 3cm is:
3^3 = 27.
How many vertices in a tetrahedron?
Fact.
Two complementary angles are in the ratio 2 : 3. What is the larger angle?
Complementary angles add up to 90°, so 2x + 3x = 90° and x = 18°.
The larger angle = 3 × 18° = 54°.
A triangle with all angles < 90°:
Definition.
A rectangle has sides 8m and 3m. Area?
8*3=24.
What is the area of a circle with radius 7cm? (π=22/7)
πr^2 = (22/7) * 49 = 154.
The sum of exterior angles of any polygon is:
Geometric property.
A triangle has sides 5, 12, 13. This is a:
5^2+12^2 = 25+144=169=13^2.
A circle with radius 10cm, what is circumference? (π=3.14)
2 * 3.14 * 10 = 62.8.
Two supplementary angles differ by 40°. What is the smaller angle?
Supplementary angles add up to 180°. Let the angles be x and x + 40°: 2x + 40° = 180°.
So x = 70°, and the angles are 70° and 110°.
A triangle with all angles > 90°?
Sum exceeds 180°.
A rectangle has sides 12m and 4m. Area?
12*4=48.
Sides in an octagon?
8 sides.
What is the area of a triangle with base 12cm and height 10cm?
0.5 * 12 * 10 = 60.
The circumference of a circle is 88 cm. What is its area? (Take π = 22/7)
Circumference = 2πr, so r = 88 ÷ (2 × 22/7) = 14 cm.
Area = πr² = 22/7 × 14 × 14 = 616 cm².
A rectangular field has length 20m and width 10m. What is the area?
20 * 10 = 200.
A square has area 81m^2. Side is:
sqrt(81) = 9.
How many faces in a triangular pyramid?
3 sides + 1 base = 4.
How many vertices has a cube?
Fact.
How many edges in a square pyramid?
4 base + 4 side edges.
If the radius of a sphere is 3 cm, what is its volume? (V=4/3*pi*r^3)
4/3 * pi * 3^3 = 4/3 * 27 * pi = 36pi.
How many edges has a tetrahedron?
Fact.
A rectangle length is 12m, area is 48m^2. What is the width?
W = 48 / 12 = 4m.
A dodecagon has how many sides?
Definition.
A cylinder radius 2, height 7. Volume (pi*r^2*h)?
(22/7)*4*7 = 88.
The sum of angles in a heptagon is:
(7-2)*180 = 5*180 = 900°.
A circle radius 7cm. Circumference (2*pi*r)?
2*(22/7)*7 = 44.
If a triangle angles are 60, 60, x, what is x?
180 - 120 = 60.
A square has perimeter 40m. What is the area?
Side=10. Area=10*10=100.
A triangle has sides 6, 8, 10. Area?
0.5 * 6 * 8 = 24.
Sum of interior angles of a pentagon:
(5-2)*180 = 540°.
A rectangle has width 4, area 20. Length is:
Area = L*W => 20=L*4 => L=5.
A rectangle has a length of 10cm and width 8cm. What is the perimeter?
2*(L+W) = 2*(10+8) = 36.
If a triangle has sides 3, 4, 5, it is a:
3^2 + 4^2 = 5^2 (9+16=25).
A circle has a diameter of 14cm. What is the area? (pi=22/7)
r = 7. Area = pi*r^2 = (22/7)*49 = 154.
A rectangle has sides 10m and 5m. Area?
10*5=50.
A triangle with all sides unequal is called:
Definition.
The area of a circle with radius 10 (pi=3.14) is:
3.14 * 100 = 314.
How many edges has a cylinder?
Circular edges at top/bottom.
The perimeter of a square is 20m. Side is:
20/4 = 5.
The two shorter sides of a right-angled triangle are 9 cm and 12 cm. What is the length of the hypotenuse?
By Pythagoras' theorem, hypotenuse² = 9² + 12² = 81 + 144 = 225.
So the hypotenuse = √225 = 15 cm.
What is the total surface area of a cube with an edge of 5 cm?
A cube has 6 square faces, so total surface area = 6a².
6 × 5² = 6 × 25 = 150 cm². (125 cm³ is its volume.)
If the radius of a circle is doubled, its area becomes:
Area = pi*r^2. (2r)^2 = 4r^2.
If a square has an area of 64 cm^2, what is its perimeter?
Side = 8. Perimeter = 4*8 = 32.
What is the sum of angles in a hexagon?
(6-2)*180 = 720°.
If a triangle has angles 45, 45, x, what is x?
180 - 90 = 90.
The number of faces in a square pyramid is:
4 triangles + 1 base = 5.
A rectangle has a length 6 and width 4. What is the area?
6*4=24.
A triangle has base 10cm, height 5cm. Area?
0.5 * 10 * 5 = 25.
If the radius of a circle is doubled, its area becomes how many times the original area?
Area = πr². If the radius becomes 2r, the new area = π(2r)² = 4πr².
So the area becomes 4 times the original, while the circumference only doubles.
A polygon with 6 sides is called:
Definition.
If a circle’s diameter is 14 cm, what is the circumference? (pi=22/7)
pi*d = (22/7)*14 = 44.
What is the angle in a semi-circle?
Geometric property.
A rectangular room is 4m by 3m. What is the area?
4*3=12.
A rectangle has sides 5m and 2m. Perimeter is:
2*(5+2)=14.
Total number of faces in a tetrahedron?
4 faces.
What is the length of the diagonal of a rectangle with sides 6 cm and 8 cm?
sqrt(6^2+8^2) = sqrt(36+64) = 10.
A cube has 6 faces. How many edges?
Geometric property.
Volume of a cube with side 5 cm?
5^3 = 125.
Angle of an equilateral triangle?
180/3 = 60.
Area of rectangle 8×6?
8*6=48.
Radius halved, area becomes?
r^2 -> (r/2)^2 = r^2/4.
If the area of a circle is 154 cm^2 (pi=22/7), find the radius.
pi*r^2 = 154 => (22/7)r^2 = 154 => r^2 = 49 => r=7.
Area of a parallelogram with base 10 and altitude 7?
Area = base * altitude = 10 * 7 = 70.
If side of a cube is tripled, its volume becomes?
3^3 = 27.
Volume of cylinder with radius 7cm and height 10cm is (pi=22/7):
- Volume of a cylinder = πr²h = (22/7) × 7² × 10 = (22/7) × 49 × 10 = 1540.
- The unit is cubic centimetres, so the complete answer is 1540 cm³.
- Use π = 22/7 exactly as the question states. Using 3.14 gives 1538.6, which is close but not the listed value.
- Volume depends on the square of the radius, so a radius of 14 cm would give four times the volume, 6160 cm³.
- Doubling only the height to 20 cm simply doubles the volume to 3080 cm³.
Complement of 30° is:
90 - 30 = 60°.
Perimeter of rectangle with length 15m and width 10m?
2(15+10) = 50.
Area of a square with diagonal 10m?
Area = 0.5 * d^2 = 50.
If radius is tripled, area becomes?
3^2 = 9.
What is the volume of a cube with side 4 cm?
Volume = side^3 = 4^3 = 64.
Area of a parallelogram with base 6 and height 4?
Area = base * height = 6 * 4 = 24.
If side of square is doubled, area becomes?
Area proportional to side^2. 2^2 = 4.
The area of a circle is 616 cm². Find the radius.
pi * r^2 = 616 => (22/7)*r^2 = 616 => r^2 = 196 => r = 14.
Area of a triangle with base 8cm and height 5cm.
Area = 0.5 * 8 * 5 = 20.
If radius of a cylinder is doubled, volume becomes how many times?
Volume proportional to r^2. (2r)^2 = 4r^2.
Radius of a cylinder is 7 cm and height is 10 cm. Find the curved surface area.
- Curved surface area of a cylinder = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm².
- The 7 in the radius cancels the 7 in 22/7, which is why exam setters choose a radius of 7 or 14.
- Curved surface area covers only the side of the cylinder, so the two circular ends are left out.
- Add the two ends and you get the total surface area: 2πrh + 2πr² = 440 + 308 = 748 cm².
- The answer must be in square centimetres, because surface area is a two-dimensional measure.
The area of a circle is 616 cm². Find the circumference.
Area = 22/7 * r^2 = 616 => r^2 = 196 => r = 14. Circumference = 2 * 22/7 * 14 = 88.
Area of triangle with base 10 and height 6?
- Area of a triangle = ½ × base × height = ½ × 10 × 6 = 30.
- Option D 60 is base × height, which is the area of a rectangle sharing the same base and height.
- A triangle covers exactly half of that rectangle, and that is where the ½ in the formula comes from.
- Any side may be taken as the base, provided the height is measured at a right angle to it.
- If the base and height are in centimetres the area is in square centimetres, so the full answer is 30 cm².
If side of cube is doubled, volume becomes how many times?
- Volume of a cube is side³, so doubling the side multiplies the volume by 2³ = 8.
- Try real numbers: a 3 cm cube holds 27 cm³ while a 6 cm cube holds 216 cm³, which is 8 times as much.
- Option A 2 is the factor for length alone, because only one dimension is compared there.
- Surface area behaves differently and grows by 2² = 4, since area uses two dimensions instead of three.
- General rule: scaling every side by k changes the volume by k³ and the surface area by k².
The perimeter of a rectangular field is 120 m and its length is 35 m. What is its area?
Perimeter = 2(L + W) => 120 = 2(35 + W) => 35 + W = 60 => W = 25 m. Area = L * W = 35 * 25 = 875 m².
The volume of a right circular cylinder is 1540 cm³ and its height is 10 cm. Find its radius. (Use pi = 22/7)
Volume = pi * r^2 * h => 1540 = (22/7) * r^2 * 10 => 154 = (22/7) * r^2 => r^2 = 49 => r = 7 cm.
The area of a circle is 154 cm². Find its circumference. (Use pi = 22/7)
Area = pi * r^2 = 154 => (22/7) * r^2 = 154 => r^2 = 49 => r = 7 cm. Circumference = 2 * pi * r = 2 * (22/7) * 7 = 44 cm.
The parallel sides of a trapezium are 12 cm and 18 cm, and its area is 150 cm². Find the height of the trapezium.
Area = 0.5 * (a + b) * h => 150 = 0.5 * (12 + 18) * h => 150 = 15 * h => h = 10 cm.
If the radius of a sphere is doubled, by what factor does its volume increase?
Volume of sphere is proportional to r^3. If radius becomes 2r, volume becomes (2r)^3 = 8 * r^3, which is 8 times.
The area of a square is equal to the area of a circle with radius 7 cm. Find the side of the square. (Use pi = 22/7)
Area of circle = (22/7) * 7 * 7 = 154 cm². Side of square = sqrt(154) ≈ 12.41 cm.
The base of a triangle is 15 cm and height is 12 cm. Find the height of another triangle of double the area whose base is 20 cm.
Area of first triangle = 0.5 * 15 * 12 = 90 cm². Area of second triangle = 2 * 90 = 180 cm². For second triangle: 0.5 * 20 * h = 180 => 10h = 180 => h = 18 cm.
Find the volume of a sphere whose surface area is 616 cm². (Use pi = 22/7)
Surface Area = 4 * pi * r^2 = 616 => 4 * (22/7) * r^2 = 616 => (88/7) * r^2 = 616 => r^2 = 49 => r = 7 cm. Volume = (4/3) * pi * r^3 = (4/3) * (22/7) * 343 = 4312 / 3 ≈ 1437.33 cm³.
The ratio of the area of a square to that of the square drawn on its diagonal is:
Let side of square = a. Area = a^2. Length of diagonal = a*sqrt(2). Area of square on diagonal = (a*sqrt(2))^2 = 2a^2. Ratio = a^2 : 2a^2 = 1 : 2.
The area of a rhombus is 120 cm² and one of its diagonals is 10 cm. Find the length of the other diagonal.
Area of rhombus = 0.5 * d1 * d2 => 120 = 0.5 * 10 * d2 => 5 * d2 = 120 => d2 = 24 cm.
The ratio of the volumes of two cubes is 27 : 64. What is the ratio of their surface areas?
Ratio of volumes = a1^3 : a2^3 = 27 : 64 => Ratio of sides = a1 : a2 = 3 : 4. Ratio of surface areas = 6*a1^2 : 6*a2^2 = 3^2 : 4^2 = 9 : 16.
The circumference of a circle exceeds its diameter by 30 cm. Find the radius of the circle. (Use pi = 22/7)
2*pi*r - 2r = 30 => 2r*(pi - 1) = 30 => 2r*(22/7 - 1) = 30 => 2r*(15/7) = 30 => 30r / 7 = 30 => r = 7 cm.
The sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. What is the area of the triangle?
3x + 4x + 5x = 144 => 12x = 144 => x = 12. Sides are 36, 48, 60. Since 36^2 + 48^2 = 60^2, it is a right-angled triangle. Area = 0.5 * 36 * 48 = 864 cm².
Find the total surface area of a hemisphere with radius 7 cm. (Use pi = 22/7)
Total surface area of hemisphere = 3 * pi * r^2 = 3 * (22/7) * 49 = 3 * 22 * 7 = 462 cm².
A rectangular plot 100 m long and 80 m wide has a path 5 m wide all around inside it. Find the area of the path.
Outer area = 100 * 80 = 8000 m². Inner length = 100 - 10 = 90 m, Inner width = 80 - 10 = 70 m. Inner area = 90 * 70 = 6300 m². Area of path = 8000 - 6300 = 1700 m².
What is the height of an equilateral triangle with side length 10 cm?
Height = (sqrt(3) / 2) * side = (sqrt(3) / 2) * 10 = 5*sqrt(3) cm.
If the ratio of radii of two cylinders is 2:3 and their heights are in the ratio 5:3, find the ratio of their volumes.
V1 / V2 = (r1^2 * h1) / (r2^2 * h2) = (2^2 * 5) / (3^2 * 3) = (4 * 5) / (9 * 3) = 20 / 27.
The perimeter of a square is equal to the circumference of a circle. If the side of the square is 22 cm, find the radius of the circle.
Perimeter of square = 4 * 22 = 88 cm. Circumference = 2 * (22/7) * r = 88 => 44/7 * r = 88 => r = 14 cm.
Find the perimeter of a semi-circle with radius 14 cm. (Use pi = 22/7)
Perimeter of semi-circle = pi * r + 2r = (22/7) * 14 + 2(14) = 44 + 28 = 72 cm.
What is the total surface area of a cube whose volume is 512 cm³?
Volume = a^3 = 512 => a = 8 cm. Total surface area = 6 * a^2 = 6 * 64 = 384 cm².
The lengths of two parallel sides of a trapezium are 10 cm and 16 cm, and the distance between them is 8 cm. What is its area?
Area of trapezium = 0.5 * (a + b) * h = 0.5 * (10 + 16) * 8 = 0.5 * 26 * 8 = 104 cm².
If a regular polygon has 12 sides, what is the measure of each interior angle?
Interior angle = [(n - 2) * 180°] / n = [(10) * 180°] / 12 = 1800 / 12 = 150°.
Find the curved surface area of a cone with base radius 7 cm and slant height 25 cm. (Use pi = 22/7)
Curved Surface Area = pi * r * l = (22/7) * 7 * 25 = 22 * 25 = 550 cm².
Find the curved surface area of a cylinder with radius 7 cm and height 10 cm. (Use pi = 22/7)
Curved Surface Area = 2 * pi * r * h = 2 * (22/7) * 7 * 10 = 440 cm².
What is the area of a right-angled isosceles triangle with hypotenuse 10 cm?
In right isosceles triangle with equal legs x: x^2 + x^2 = 10^2 => 2x^2 = 100 => x^2 = 50. Area = 0.5 * x^2 = 0.5 * 50 = 25 cm².
The sum of interior angles of a regular polygon is 1080°. How many sides does it have?
Sum = (n - 2) * 180° = 1080° => n - 2 = 1080 / 180 = 6 => n = 8.
If the side of an equilateral triangle is 8 cm, what is its area?
Area of equilateral triangle = (sqrt(3) / 4) * side^2 = (sqrt(3) / 4) * 64 = 16*sqrt(3) cm².
A ladder 10 m long reaches a window 8 m above the ground. How far is the foot of the ladder from the base of the wall?
Distance = Sqrt(10^2 - 8^2) = Sqrt(100 - 64) = Sqrt(36) = 6 m.
Find the diagonal of a square whose area is 128 cm².
Area of square = d^2 / 2 = 128 => d^2 = 256 => d = 16 cm.
Find the perimeter of a sector of a circle with radius 14 cm and central angle 90°. (Use pi = 22/7)
Arc length = (90/360) * 2 * (22/7) * 14 = (1/4) * 88 = 22 cm. Perimeter of sector = Arc length + 2 * radius = 22 + 2(14) = 22 + 28 = 50 cm.
Find the length of the longest rod that can be placed in a room of dimensions 10 m x 10 m x 5 m.
Diagonal of cuboid = Sqrt(l^2 + b^2 + h^2) = Sqrt(10^2 + 10^2 + 5^2) = Sqrt(100 + 100 + 25) = Sqrt(225) = 15 m.
Find the area of a circle inscribed in a square of side 14 cm. (Use pi = 22/7)
Diameter of inscribed circle = side of square = 14 cm => Radius r = 7 cm. Area = pi * r^2 = (22/7) * 7^2 = 154 cm².
Each interior angle of a regular polygon is 144°. How many sides does the polygon have?
Exterior angle = 180° - 144° = 36°. Number of sides n = 360° / Exterior angle = 360° / 36° = 10.
The perimeter of a rhombus is 40 cm and one of its diagonals is 12 cm. Find the area of the rhombus.
Side of rhombus = 40 / 4 = 10 cm. Half of diagonal d1/2 = 6 cm. Half of second diagonal d2/2 = Sqrt(10^2 - 6^2) = 8 cm => d2 = 16 cm. Area = 0.5 * d1 * d2 = 0.5 * 12 * 16 = 96 cm².
A solid copper sphere of radius 6 cm is melted and recast into a wire of radius 0.1 cm. Find the length of the wire.
Volume of sphere = (4/3)*pi*r^3 = (4/3)*pi*216 = 288*pi cm³. Volume of cylinder wire = pi*r^2*h = pi*(0.1)^2*h = 0.01*pi*h. Equating: 0.01*h = 288 => h = 28,800 cm = 288 m.
Find the length of the altitude of an equilateral triangle with side length 12 cm.
Altitude h = (sqrt(3)/2) * side = (sqrt(3)/2) * 12 = 6*sqrt(3) cm.
Find the area of a sector of a circle of radius 6 cm with a central angle of 60°. (Use pi = 22/7)
Area of sector = (theta / 360°) * pi * r^2 = (60 / 360) * (22/7) * 36 = (1/6) * (22/7) * 36 = 6 * (22/7) = 132 / 7 = 18.86 cm².
Find the length of the diagonal of a rectangle with length 12 cm and width 5 cm.
Diagonal = Sqrt(length^2 + width^2) = Sqrt(12^2 + 5^2) = Sqrt(144 + 25) = Sqrt(169) = 13 cm.
What is the area of an isosceles right triangle with equal sides of length 8 cm?
Area = 0.5 * base * height = 0.5 * 8 * 8 = 32 cm².
Find the perimeter of a semicircle with a radius of 7 cm. (Use pi = 22/7)
Perimeter of semicircle = pi * r + 2r = (22/7) * 7 + 2(7) = 22 + 14 = 36 cm.
What is the third angle of a triangle if its other two angles are 55° and 65°?
Sum of angles in a triangle = 180°. Third angle = 180° - (55° + 65°) = 180° - 120° = 60°.
Find the angle subtended by a major arc of a circle if the minor arc subtends 110° at the center.
Total angle around center = 360°. Major arc angle = 360° - 110° = 250°.
Find the surface area of a cube with side length 5 cm.
Total surface area of a cube = 6 * side^2 = 6 * (5^2) = 6 * 25 = 150 cm².
What is the length of the hypotenuse of a right-angled triangle with leg lengths 9 cm and 12 cm?
Hypotenuse = Sqrt(9^2 + 12^2) = Sqrt(81 + 144) = Sqrt(225) = 15 cm.
If the circumference of a circle is 88 cm, find its radius. (Use pi = 22/7)
Circumference = 2 * pi * r => 88 = 2 * (22/7) * r => 88 = (44/7) * r => r = (88 * 7)/44 = 14 cm.
If the diagonal of a square is 8*sqrt(2) cm, what is its area?
Diagonal = side * sqrt(2) => side = 8 cm. Area = side^2 = 8^2 = 64 cm².
A wheel has a radius of 21 cm. How many revolutions will it make to cover a distance of 1320 cm?
Circumference = 2 * (22/7) * 21 = 132 cm. Revolutions = Total Distance / Circumference = 1320 / 132 = 10.
Find the area of a right triangle with base 14 cm and height 10 cm.
Area = 0.5 * Base * Height = 0.5 * 14 * 10 = 70 cm².
What is the total surface area of a sphere of radius 7 cm? (Use pi = 22/7)
Total Surface Area = 4 * pi * r^2 = 4 * (22/7) * 7^2 = 4 * 22 * 7 = 616 cm².
What is the area of a rectangle whose perimeter is 36 cm and length is 10 cm?
Perimeter = 2(L + W) => 36 = 2(10 + W) => 18 = 10 + W => W = 8 cm. Area = L * W = 10 * 8 = 80 cm².
What is the volume of a cube whose side length is 6 cm?
Volume of a cube = side^3 = 6^3 = 216 cm³.
Find the perimeter of an equilateral triangle with an area of 9*sqrt(3) cm².
Area of equilateral triangle = (sqrt(3)/4) * a^2 = 9*sqrt(3) => a^2 = 36 => a = 6 cm. Perimeter = 3 * a = 3 * 6 = 18 cm.
The complement of an angle measuring 35° is:
Complementary angles sum to 90°. Complement of 35° = 90° - 35° = 55°.
What is the perimeter of a rectangle with length 15 cm and breadth 9 cm?
Perimeter = 2 * (length + breadth) = 2 * (15 + 9) = 2 * 24 = 48 cm.
Find the diagonal of a square of side 10 cm.
Diagonal of a square = side * sqrt(2) = 10*sqrt(2) cm.
If a polygon has 8 sides (octagon), how many diagonals does it have?
Number of diagonals in an n-sided polygon = n(n - 3) / 2 = 8(8 - 3) / 2 = 8 * 5 / 2 = 20.
The surface area of a sphere is 616 cm². Find its radius. (Use pi = 22/7)
Surface Area = 4 * pi * r^2 => 616 = 4 * (22/7) * r^2 => 616 = (88/7) * r^2 => r^2 = (616 * 7) / 88 = 49 => r = 7 cm.
The perimeter of a rectangle is 60 cm. If its length is twice its width, what is the area of the rectangle?
2(L + W) = 60 => 2(2W + W) = 60 => 6W = 60 => W = 10, L = 20. Area = L * W = 20 * 10 = 200 cm².
What is the cost of carpeting a room 15 m long and 8 m wide at Rs. 25 per square meter?
Area = Length * Width = 15 * 8 = 120 m². Cost = 120 * 25 = Rs. 3000.
What total distance will a wheel of diameter 70 cm cover in 100 revolutions? (Use pi = 22/7)
Circumference = pi * d = (22/7) * 70 cm = 220 cm = 2.2 m. Distance in 100 revs = 2.2 * 100 = 220 meters.
If the ratio of the areas of two squares is 16:25, what is the ratio of their perimeters?
Area ratio = a1^2 / a2^2 = 16/25 => Side ratio a1/a2 = 4/5. Perimeter ratio is equal to side ratio = 4:5.
What is the area of a right-angled triangle with a base of 12 cm and a hypotenuse of 13 cm?
Using Pythagoras theorem: Height² = Hypotenuse² − Base² = 13² − 12² = 169 − 144 = 25. Thus, Height = 5 cm. Area = 0.5 × Base × Height = 0.5 × 12 × 5 = 30 cm².
The diagonal of a square field is 20 meters. What is the area of the square field?
The area of a square can be calculated directly from its diagonal (d) using Area = d² / 2. Here, d = 20 meters, so Area = 20² / 2 = 400 / 2 = 200 m².
In an isosceles triangle, if the vertex angle is 80°, what is the measure of each base angle?
Sum of base angles = 180° - 80° = 100°. Each base angle = 100° / 2 = 50°.
What is the volume of a cylinder with radius 3 cm and height 7 cm? (Use pi = 22/7)
Volume = pi * r^2 * h = (22/7) * (3)^2 * 7 = 22 * 9 = 198 cm³.
Find the area of a rhombus whose diagonals are 12 cm and 16 cm.
Area of rhombus = (1/2) * d1 * d2 = (1/2) * 12 * 16 = 6 * 16 = 96 cm².
What is the measure of each interior angle of a regular octagon?
Interior angle = [(n - 2) * 180°] / n. For n = 8: [(6) * 180°] / 8 = 1080° / 8 = 135°.
The sides of a triangle are 3 cm, 4 cm, and 5 cm. What is its area?
This is a right-angled triangle since 3^2 + 4^2 = 5^2. Area = (1/2) * 3 * 4 = 6 cm².
Find the perimeter of a rectangle whose length is 12 cm and breadth is 8 cm.
Perimeter = 2 * (length + breadth) = 2 * (12 + 8) = 2 * 20 = 40 cm.
The diagonal of a square is 10*sqrt(2) cm. What is its side length?
Diagonal d = a * sqrt(2). Given d = 10*sqrt(2), equating gives a * sqrt(2) = 10*sqrt(2) => side a = 10 cm.
What is the area of a right-angled triangle with base 10 cm and height 12 cm?
Area = (1/2) * base * height = (1/2) * 10 * 12 = 60 cm².