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

Directions: In this question, you have to decide which of the statements I, II and III is/are required for determining the answer to the given question. What is the capacity of the cylindrical tank? I. The base area is 87,400 sq.cm. II. The height of the tank is 4.5 times its radius. III. The base circumference is 960 cm.

  1. Only II and III

  2. Only II and either I or III

  3. Either I or III

  4. Only I and II

  5. All I, II and III
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Capacity of a cylinder = pi * r^2 * h. Statement I gives base area (pi * r^2). Statement II gives h = 4.5r. Statement III gives circumference (2 * pi * r). We need both r and h. I gives pi * r^2, so we can find r. Then II gives h. Alternatively, III gives r, then II gives h. Thus, II and either I or III is sufficient.

Multiple choice

In a research facility, a cylindrical tank containing water has a total volume of 864π cubic meters. The researchers plan to transfer this water into four conical flasks. Each conical flask has the same radius as that of the cylindrical tank. However, the height of each conical flask is three times the radius of the conical flask. What is the height, in meters, of each conical flask?

  1. 6

  2. 12

  3. 18

  4. 24
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of the cylinder is 864pi. The volume of one cone is (1/3) * pi * r^2 * h. Since h = 3r, the volume of one cone is (1/3) * pi * r^2 * (3r) = pi * r^3. Four such cones have a total volume of 4 * pi * r^3. Equating 4 * pi * r^3 = 864pi, we get r^3 = 216, so r = 6. Since h = 3r, h = 3 * 6 = 18.

Multiple choice

A toy consists of a cone surmounted by a hemisphere. The cone has a radius of 8 centimeters and a height of 15 centimeters. The hemisphere has the same radius as the cone. What is the approximate volume of the toy?

  1. 341.33π cubic centimeters

  2. 541.33π cubic centimeters

  3. 661.33π cubic centimeters

  4. 681.33π cubic centimeters
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * 64 * 15 = 320 * pi. Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * pi * 512 = 341.33 * pi. Total volume = 320 * pi + 341.33 * pi = 661.33 * pi.

Multiple choice

Directions: In the following item, Quantity I and Quantity II are given. Determine the relationship between the quantities and choose the appropriate option. Quantity I: Area of a circle with radius 7 cm Quantity II: Three times the area of a triangle with base 14 cm and height 7 cm

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II, or No relation
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: pi * 7^2 = 49 * 3.14 = 153.86. Quantity II: 3 * (1/2 * 14 * 7) = 3 * 49 = 147. Since 153.86 > 147, Quantity I > Quantity II.