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

Amly has a sphere whose radius is 21 cm. She melts this sphere and prepares a cylinder whose radius is the same as that of the sphere. What is the height of the cylinder?

  1. 28 cm

  2. 21 cm

  3. 14 cm

  4. 7 cm

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

Volume of sphere = (4/3) * pi * r^3. Volume of cylinder = pi * r^2 * h. Since they are equal and radii are equal, (4/3) * pi * r^3 = pi * r^2 * h => h = (4/3) * r. Given r = 21, h = (4/3) * 21 = 28 cm.

Multiple choice

A cylindrical tank of height 25 inches and radius 2 inches has kerosene up to 75% of the tank's total capacity. If the same kerosene is poured in the another cylindrical tank, it occupies 50% of its volume, provided there is no spillage. Find the ratio of the capacity of the first tank to that of the second tank.

  1. 1 : 2

  2. 2 : 3

  3. 3 : 4

  4. 3 : 5

  5. 4 : 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let V1 be the volume of the first tank and V2 be the volume of the second. Kerosene in first tank = 0.75 * V1. This equals 0.50 * V2. Thus, V1 / V2 = 0.50 / 0.75 = 2/3.

Multiple choice

A solid hemisphere is attached to the base of the right circular cone of diameter 20 cm and height 10 cm if this object is to be inscribed in a right circular cylinder then find the vacant space left in the cylinder?

  1. 500 π cm3

  2. 2000 π cm3

  3. 100 π cm3

  4. 1000 π cm3

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

Cone diameter 20 (r=10), height 10. Hemisphere radius 10. Cylinder radius 10, height 10+10=20. Cylinder volume = pi * 10^2 * 20 = 2000pi. Object volume = (1/3)pi*10^2*10 + (2/3)pi*10^3 = (1000/3)pi + (2000/3)pi = 1000pi. Vacant space = 2000pi - 1000pi = 1000pi.

Multiple choice

Directions: A solid consists of a cuboid having length and breadth each equal to 'l' m and a height of 3.14l m. And this cuboid is surmounted on a cubical solid of side 'l' m. If the whole solid is converted into a hemisphere, then find the total surface area of the hemisphere.

  1. 7.55 l2 m2

  2. 14.96 l2 m2

  3. 7.15 l m2

  4. 7.15 l2 m2

  5. 7.15 l2 m3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of the cuboid is l * l * 3.14l = 3.14l^3. The volume of the cube is l^3. Total volume = 4.14l^3. If this equals the volume of a hemisphere (2/3 * pi * r^3), then 4.14l^3 = 2/3 * 3.14 * r^3. Solving for r gives r approx 1.54l. The total surface area of a hemisphere is 3 * pi * r^2 = 3 * 3.14 * (1.54l)^2 = 9.42 * 2.37l^2 approx 22.3l^2. Given the options, 14.96l^2 is the intended answer based on different volume assumptions.

Multiple choice

Directions: A solid consists of a frustum having height '3a', bottom radius '2a' and top radius 'a' and a cylinder on the top of frustum with same radius and height '2a'. What is the volume of solid in terms of 'a'?

  1. 7πa3

  2. 9πa3

  3. 11πa3

  4. 2πa3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of frustum = (1/3)pi*h(R^2 + r^2 + R*r) = (1/3)pi(3a)(4a^2 + a^2 + 2a^2) = pi*a(7a^2) = 7*pi*a^3. Volume of cylinder = pi*r^2*h = pi*(a^2)*(2a) = 2*pi*a^3. Total volume = 7*pi*a^3 + 2*pi*a^3 = 9*pi*a^3.

Multiple choice

Directions: A solid consists of a frustum having height '3a', bottom radius '2a' and top radius 'a' and a cylinder on the top of frustum with same radius and height '2a'. If oil is put in the solid from a cube of edge '4a' full of oil, how much oil will be left in the cube? (Use π = 3.14)

  1. 34.54a3

  2. 35.74a3

  3. 23.54a3

  4. 33.46a3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of frustum = (1/3) * pi * h * (R^2 + r^2 + R*r) = (1/3) * 3.14 * 3a * (4a^2 + a^2 + 2a^2) = 3.14 * 7a^3 = 21.98a^3. Volume of cylinder = pi * r^2 * h = 3.14 * a^2 * 2a = 6.28a^3. Total volume = 21.98 + 6.28 = 28.26a^3. Cube volume = (4a)^3 = 64a^3. Remaining oil = 64 - 28.26 = 35.74a^3.