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 metallic sphere of radius 6.3 cm is melted and recast into a right circular cone of height 25.2 cm. What is the ratio of the diameter of the base to the height of the cone?

  1. 2 : 1

  2. 3 : 2

  3. 1 : 2

  4. 2 : 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of sphere = (4/3)pi*r^3 = (4/3)*pi(6.3)^3. Volume of cone = (1/3)pi*R^2*h = (1/3)*pi*R^2(25.2). Equating volumes: 4*(6.3)^3 = R^2*(25.2). Solving for R: R^2 = (4 * 6.3 * 6.3 * 6.3) / 25.2 = 6.3 * 6.3, so R = 6.3. The diameter is 2*R = 12.6. The ratio of diameter to height is 12.6 / 25.2 = 1/2.

Multiple choice

In a building there are 30 cylindrical pillars. The radius of each pillar is 35 cm and height is 5 m. Find out the cost of painting the curved surface of half the number of pillars. The rate of painting is Rs. 10 per m2.

  1. Rs. 1650

  2. Rs. 16,500

  3. Rs. 4125

  4. Rs. 8250
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Curved surface area of one pillar = 2 * pi * r * h = 2 * pi * 0.35 * 5 = 3.5 * pi = 11 m^2 (approx). Half pillars = 15. Total area = 15 * 11 = 165 m^2. Cost = 165 * 10 = 1650.

Multiple choice

A square is drawn such that its vertices are lying on a circle of radius 201 mm. What is the ratio of area of circle to that of square?

  1. 11 : 7

  2. 7 : 11

  3. 20 : 19

  4. 19 : 20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Radius R = 201. Square diagonal = 2R = 402. Side of square s = 402 / sqrt(2) = 201 * sqrt(2). Area of circle = pi * R^2 = pi * 201^2. Area of square = s^2 = 2 * 201^2. Ratio = (pi * 201^2) / (2 * 201^2) = pi / 2. Using pi = 22/7, ratio = (22/7) / 2 = 11/7.

Multiple choice

A thin rod of length 24 feet is cut into rods of equal size and joined so as to form a skeleton cube. What is the area of one of the faces of the largest cube thus constructed?

  1. 25 square feet

  2. 24 square feet

  3. 9 square feet

  4. 4 square feet
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A cube has 12 edges. If the total length of the rod is 24 feet, each edge of the cube is 24/12 = 2 feet. The area of one face of a cube with side length s is s^2. Thus, 2^2 = 4 square feet.