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 cylinder having diameter 32 cm and height 4 cm is melted to make 24 spheres out of it of the same size. Find out the radius of each sphere.

  1. 3.1 cm

  2. 4.17 cm

  3. 3 cm

  4. 3.17 cm

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

Volume of cylinder = pi * r^2 * h = pi * 16^2 * 4 = 1024 * pi. Volume of 24 spheres = 24 * (4/3) * pi * r_s^3 = 32 * pi * r_s^3. Equating them: 1024 * pi = 32 * pi * r_s^3, so r_s^3 = 32, r_s = cube root of 32, which is approximately 3.1748 cm.

Multiple choice

Directions: In these questions, two equations numbered I and II are given. You have to solve both the equations and give answer (a) x ≥ y (b) x ≤ y (c) x y (e) x = y or Relationship between x and y cannot be established A right cylindrical vessel is full with water. Height = 20 cm, Radius 5 cm. (x) How many right cones having the same diameter and height as that of the right cylinder will be needed to store that water? (take π = 22/7) (y) 5

  1. a

  2. b

  3. c

  4. d

  5. e
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Directions: You are given two quantities, Quantity I and Quantity II. Compare the two quantities and choose the correct option accordingly. Quantity I: Magnitude of volume of a cylinder of radius 3.5 m and height 10 m Quantity II: Magnitude of total surface area of a cylinder of radius 3 m and height 20 m

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I = Quantity II

  4. No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I (Volume of cylinder) = pi*r^2*h = pi*(3.5^2)10 = pi*12.25*10 = 122.5*pi. Quantity II (Total surface area) = 2*pi*r(r+h) = 2*pi*3*(3+20) = 6*pi*23 = 138*pi. 122.5*pi < 138*pi.

Multiple choice

What is the area of the circle, the coordinates of the end points of whose diameter are ( − 2 , − 3 2 ) and ( 2 , 3 2 ) ?

  1. 5 π sq. units

  2. 10 π sq. units

  3. 25 4 π sq. units

  4. 25 π sq. units
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The diameter endpoints are (-2, -1.5) and (2, 1.5). The length of the diameter is sqrt((2 - -2)^2 + (1.5 - -1.5)^2) = sqrt(4^2 + 3^2) = sqrt(16+9) = 5. The radius is 2.5. Area = pi * r^2 = pi * (2.5)^2 = 6.25 * pi = 25/4 * pi.

Multiple choice

Base of a cone, hemisphere and cylinder are same and also heights of these figures are same then find the ratio of their volumes.

  1. 1 :2 :3

  2. 2 :3 : 2

  3. 3 :1: 2

  4. 3 :2 : 1

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

Volume of cone = (1/3)pi*r^2*h. Volume of hemisphere = (2/3)pi*r^3. Volume of cylinder = pi*r^2*h. Since r = h, Volume cone = (1/3)pi*r^3, Volume hemisphere = (2/3)pi*r^3, Volume cylinder = pi*r^3. Ratio = (1/3) : (2/3) : 1 = 1 : 2 : 3.