Quantitative Aptitude

Mensuration

2,507 Questions
All Direct Formula Application 1067 Shape Transformations 343 Mensuration Ratio Equations 277 Combined & Hollow Solids 247 Successive Percentage Changes 178 Inscribed & Circumscribed Figures 165 Cost Estimation Problems 100 Liquid Pour & Submergence 67 Unit Conversions 35 Path & Border Calculations 17 Time & Work Integration 7 Scale & Model Proportions 2

Mensuration Questions

Multiple choice

A cylindrical tank with radius 7 meters is filled with water up to a height of 14 meters. A conical object is submerged in the tank, with its vertex at the bottom and a base radius of 7 meters, and height equal to the water height. Find the volume of the remaining water in the tank after submerging the conical object. Assume the volume of the conical object displaces the water equally throughout the tank.

  1. 400.33a cubic meters

  2. 540n cubic meters

  3. 457.33a cubic meters

  4. 134.4 cubic meters
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

A metal recycling plant receives an iron cannonball with a radius of 2.1 decimeters from an old battleship. The company decides to melt the cannonball and reshape it into a cylindrical iron support rod for a bridge. The rod is designed with a height of 28 cm, ensuring that no iron is wasted. Find the ratio of the total surface area of the cylindrical rod to that of the original cannonball.

  1. 6 : 5

  2. 7 : 4

  3. 7 : 5

  4. 7 : 6

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Cannonball r = 2.1 dm = 21 cm. Volume = (4/3) * pi * 21^3. Surface area = 4 * pi * 21^2. Cylinder: Volume = pi * r_c^2 * 28 = (4/3) * pi * 21^3. r_c^2 = (4 * 9261) / (3 * 28) = 441. r_c = 21. Surface area = 2 * pi * r_c * (r_c + h) = 2 * pi * 21 * (21 + 28) = 2 * pi * 21 * 49. Ratio = (2 * pi * 21 * 49) / (4 * pi * 21^2) = (2 * 49) / (4 * 21) = 98 / 84 = 7/6.

Multiple choice

A group of craftsmen is tasked with creating decorative half-spheres (hemispheres) from a solid block of wood shaped like a cube with a side length of 20 cm. They plan to cut out two identical hemispheres of the maximum possible size from opposite faces of the cube. What will be the total volume (in cubic centimeters) of the remaining wood after the hemispheres are cut out?

  1. 3813.33 cubic centimeters.

  2. 3057.33 cubic centimeters.

  3. 3356.67 cubic centimeters.

  4. 2106.67 cubic centimeters

  5. 4000 cubic centimeters
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Riya decides to paint a hexagonal-shaped window with each side measuring 2 metres. She wants to apply paint only to the glass area inside the window, and she plans to paint both sides of the glass. If 1 litre of paint covers 3 square metres of glass surface, to the nearest litres how many litres of paint will Riya need to buy?

  1. 2 litres

  2. 4 litres

  3. 7 litres

  4. 12 litres

  5. 16 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area of a regular hexagon = (3 * sqrt(3) / 2) * side^2. Side = 2, so Area = (3 * sqrt(3) / 2) * 4 = 6 * sqrt(3) = 10.39 sq m. Painting both sides = 20.78 sq m. Paint needed = 20.78 / 3 = 6.92 liters. Nearest liter is 7.

Multiple choice

Volume of the cylinder is 3564 m³ Radius of the cylinder is equal to the side of a square whose area is 81 sq m. Height of the cuboid is equal to the height of the cylinder. The Width of the cuboid is half of the height of the cylinder. Total surface area of the cuboid is 700 sq m. Find the volume of the cuboid.

  1. 1312 cu. m

  2. 1224 cu. m

  3. 1172 cu. m

  4. 1176 cu m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Cylinder radius = sqrt(81) = 9. Cylinder volume = pi * r^2 * h = 3564. h = 3564 / (pi * 81) = 14. Cuboid height = 14, width = 7. Surface area = 2(lw + lh + wh) = 700. 2(l*7 + l*14 + 7*14) = 700. 21l + 98 = 350. 21l = 252, l = 12. Volume = l * w * h = 12 * 7 * 14 = 1176.

Multiple choice

The surface area of a closed rectangular prism, which is inscribed in a sphere, is 2976 sq cm, and the sum of the lengths of all its edges is 404 cm. The surface area, in square cm, of the sphere is:

  1. 6056π

  2. 6236π

  3. 7225π

  4. 8181π

  5. a
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a rectangular prism with dimensions l, w, h: Surface area 2(lw + wh + lh) = 2976. Sum of edges 4(l + w + h) = 404, so l + w + h = 101. The diagonal of the prism is the diameter of the sphere, d^2 = l^2 + w^2 + h^2. We know (l+w+h)^2 = l^2+w^2+h^2 + 2(lw+wh+lh). Thus 101^2 = d^2 + 2976. 10201 = d^2 + 2976, so d^2 = 7225. The surface area of the sphere is 4 * pi * r^2 = pi * d^2 = 7225 * pi.

Multiple choice

The circumference of a circle with a radius of 14 centimeters is a centimeters and the lateral surface area of a cylinder with a radius of 9 centimeters and height of 7 centimeters is b centimeters2. Quantity A The value of 4a Quantity B The value of b

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the given information.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

a = circumference = 2 * pi * 14 = 28 * pi (approx 87.96). Quantity A = 4a = 112 * pi (approx 351.86). b = lateral surface area of cylinder = 2 * pi * r * h = 2 * pi * 9 * 7 = 126 * pi (approx 395.84). Since 126 * pi > 112 * pi, Quantity B is greater.

Multiple choice

A right circular cylinder has a radius of 5 centimeters and a height of 10 centimeters. Quantity A The volume of the cylinder (Use π = 3.14) Quantity B 800 cubic centimeters

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of a cylinder is pi * r^2 * h. Using r = 5, h = 10, and pi = 3.14, the volume is 3.14 * 25 * 10 = 785 cubic centimeters. Since 785 < 800, Quantity B is greater.

Multiple choice

Quantity A The volume of a sphere with radius 4 centimeters Quantity B The volume of a cylinder with height 8 centimeters and base radius 2 centimeters

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume A = 4/3 * pi * 4^3 = 256/3 * pi = 85.33 * pi. Volume B = pi * 2^2 * 8 = 32 * pi. Volume A is clearly greater.

Multiple choice

A cone with a base radius of 6 cm and a height of 12 cm is placed upside down in a cylindrical container. The cylindrical container has a diameter of 14 cm and a height of 15 cm. What is the remaining volume of the cylinder after the cone is placed inside it?

  1. 540π cm3

  2. 591π cm3

  3. 915π cm3

  4. 951π cm3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cylinder volume = pi * r^2 * h = pi * 7^2 * 15 = 735pi. Cone volume = (1/3) * pi * r^2 * h = (1/3) * pi * 6^2 * 12 = 144pi. Remaining volume = 735pi - 144pi = 591pi.

Multiple choice

In a workshop, an aluminum sphere with a radius of 6 cm is melted and recast into a cylindrical rod with a height of 32 cm. What is the diameter of the cylindrical rod?

  1. 2 cm

  2. 3 cm

  3. 5 cm

  4. 6 cm

  5. a
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of sphere = 4/3 * pi * r^3 = 4/3 * pi * 6^3 = 4/3 * pi * 216 = 288 * pi. Volume of cylinder = pi * r_cyl^2 * h = pi * r_cyl^2 * 32. 288 * pi = 32 * pi * r_cyl^2 => r_cyl^2 = 288 / 32 = 9. r_cyl = 3. Diameter = 2 * 3 = 6 cm.

Multiple choice

The sum of the edge lengths of two cubes is 10 units, and the sum of the volumes of both the cubes is 280 cubic units. Find the sum of the surface areas of both the cubes.

  1. 90 square units

  2. 100 square units

  3. 216 square units

  4. 312 square units

  5. 512 square units
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let edges be x and y. x+y = 10, x^3 + y^3 = 280. x^3 + y^3 = (x+y)(x^2 - xy + y^2) = 10((x+y)^2 - 3xy) = 280. 100 - 3xy = 28. 3xy = 72, xy = 24. x^2 + y^2 = (x+y)^2 - 2xy = 100 - 48 = 52. Sum of surface areas = 6x^2 + 6y^2 = 6(52) = 312.