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 is in the form of a cylinder with hemispherical ends. The total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. The surface area of the solid is

  1. 16 cm2

  2. 418 cm2

  3. 485 cm2

  4. 16.6 cm2

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

The solid consists of a cylinder (height 19 - 7 = 12cm, radius 3.5cm) and two hemispheres (radius 3.5cm). Surface area = 2 * pi * r * h (cylinder) + 4 * pi * r^2 (sphere) = 2 * pi * 3.5 * 12 + 4 * pi * 3.5^2 = 84pi + 49pi = 133pi = 417.8 approx 418.

Multiple choice

A metallic cylinder with 70 cm height and base diameter 15 cm is surmounted by a hemisphere of same diameter. Find the mass of the solid; given that 1 cm3 of metal has 10 g of mass (approximately). (Take π = 22/7)

  1. 135.98 kg

  2. 132.59 kg

  3. 133.58 kg

  4. 130.95 kg
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = (22/7) * 7.5^2 * 70 = 12375 cm^3. Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * (22/7) * 7.5^3 = 883.57 cm^3. Total volume = 13258.57 cm^3. Mass = 13258.57 * 10 g = 132585.7 g = 132.59 kg.

Multiple choice

The length of a room is twice its breadth. The cost of carpeting it at Re. 1 per square metre is Rs. 1800 and the cost of whitewashing only the walls at 50 paise per square metre is Rs. 265, excluding the area of doors and windows of area 10 square metres. The height of the room is

  1. 2.5 m

  2. 2.8 m

  3. 3.2 m

  4. 3 m

  5. 4 m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let breadth = x, length = 2x. Area = 2x^2. Cost of carpet = 1 * 2x^2 = 1800 -> x^2 = 900 -> x = 30. Breadth = 30, Length = 60. Wall area = 2*(L+B)H = 2(90)*H = 180H. Wall area - 10 = (265 / 0.5) = 530. 180H = 540 -> H = 3.