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 solid sphere of radius 3 cm is melted to form a hollow right circular cylindrical tube of length 4 cm and external radius 5 cm. The thickness of the tube is

  1. 1 cm

  2. 9 cm

  3. 0.6 cm

  4. 1.5 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of sphere = 4/3 * pi * 3^3 = 36 * pi. Volume of hollow cylinder = pi * h * (R^2 - r^2) = pi * 4 * (5^2 - r^2) = 4 * pi * (25 - r^2). Setting them equal: 36 = 4 * (25 - r^2), so 9 = 25 - r^2, r^2 = 16, r = 4. Thickness = R - r = 5 - 4 = 1 cm.

Multiple choice

A cylindrical vessel, whose radius is 6 cm, contains water. If a solid sphere of radius 3 cm is dipped into the vessel completely, then what is the rise in the water level in the vessel?

  1. 3 cm

  2. 2 cm

  3. 1 cm

  4. 0.5 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of the sphere submerged equals the volume of the water displaced. Volume of sphere = (4/3) * pi * 3^3 = 36 * pi. Volume of water rise in cylinder = pi * r^2 * h = pi * 6^2 * h = 36 * pi * h. Equating the two: 36 * pi = 36 * pi * h, so h = 1 cm.

Multiple choice

The external and the internal radii of a hollow right circular cylinder of height 15 cm are 6.75 cm and 5.25 cm, respectively. If it is melted to form a solid cylinder of height half of the original cylinder, then the radius of the solid cylinder will be

  1. 6 cm

  2. 6.5 cm

  3. 7 cm

  4. 7.25 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of hollow cylinder = pi * h * (R^2 - r^2) = pi * 15 * (6.75^2 - 5.25^2) = pi * 15 * (6.75 - 5.25)(6.75 + 5.25) = pi * 15 * 1.5 * 12 = 270 * pi. New solid cylinder height = 15/2 = 7.5. pi * r_new^2 * 7.5 = 270 * pi. r_new^2 = 270 / 7.5 = 36. r_new = 6.

Multiple choice

A top is of the shape of a cone over a hemisphere. The radius of the hemisphere is 3 cm. The total height of the top is 7 cm. What is the total area of the top?

  1. 103.7 sq. cm

  2. 21.45 sq. cm

  3. 215.4 sq. cm

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The hemisphere radius is 3 cm, so the cone height is 7 - 3 = 4 cm. The slant height of the cone is sqrt(3^2 + 4^2) = 5 cm. Total area = (2 * pi * r^2) + (pi * r * l) = (2 * pi * 9) + (pi * 3 * 5) = 18pi + 15pi = 33pi = 33 * 3.14 = 103.62. Option A is the closest.