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 circus tent has a cylindrical base surmounted by a conical roof. The radius of the cylindrical part is 30 m and its height is 9 m. Find the volume of air contained in the tent if the total height of the tent is 24 m. Also, find the volume of air available per person if 15 persons are seated in the tent.

  1. 39,600 m3, 2640 m3

  2. 42,360 m3, 4260 m3

  3. 39,600 m3, 4260 m3

  4. 39,600 m3, 2460 m3

  5. 38,600 m3, 2460 m3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume = Volume of cylinder + Volume of cone. Cylinder: pi * 30^2 * 9 = 8100 * pi. Cone: (1/3) * pi * 30^2 * (24-9) = 4500 * pi. Total = 12600 * pi = 12600 * 3.1428... approx 39600. Per person = 39600 / 15 = 2640.

Multiple choice

A sector of circle of radius 10 cm has the angle 120o. It is rolled up so that two bounding radii are joined together to form a cone. Find the volume of the cone.

  1. 109.3 cm3

  2. 107.32 cm3

  3. 105.63 cm3

  4. 108.45 cm3

  5. 102.5 cm2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Radius of sector R = 10. Arc length L = (120/360) * 2 * pi * 10 = 20pi/3. This arc becomes the circumference of the cone base: 2 * pi * r = 20pi/3, so r = 10/3. Slant height l = R = 10. Height h = sqrt(l^2 - r^2) = sqrt(100 - 100/9) = sqrt(800/9) = 20*sqrt(2)/3. Volume = (1/3) * pi * r^2 * h = (1/3) * pi * (100/9) * (20*sqrt(2)/3) = 2000*pi*sqrt(2) / 81 = 109.3.

Multiple choice

A cone with radius 7 m has volume 1232 m3. What is the cost of painting the curved surface of the cone at the rate of Rs. 20 per m2?

  1. Rs. 7500

  2. Rs. 9000

  3. Rs. 10,500

  4. Rs. 11,000

  5. Rs. 12,700
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume V = (1/3) * pi * r^2 * h. 1232 = (1/3) * (22/7) * 7^2 * h => 1232 = (1/3) * 22 * 7 * h => h = 24. Slant height l = sqrt(r^2 + h^2) = sqrt(7^2 + 24^2) = 25. Curved surface area = pi * r * l = (22/7) * 7 * 25 = 550. Cost = 550 * 20 = 11000.

Multiple choice

A hollow metallic cylindrical tank has an internal radius of 80 cm and height 200 cm. The thickness of the metal is 1 cm. If the tank is melted and cast into a right circular cone of height 3 m, find the radius of the cone, correct to two decimal places.

  1. 13.74 cm

  2. 17.94 cm

  3. 16.64 cm

  4. 15.34 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of the hollow cylinder is pi * (R^2 - r^2) * h, where R=81 and r=80. Volume = pi * (81^2 - 80^2) * 200 = pi * 161 * 200 = 32200 * pi. Setting this equal to the cone volume (1/3) * pi * r_cone^2 * 300, we get r_cone^2 = 322, so r_cone = sqrt(322) approx 17.94.