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 right circular cone has height 6 centimeters and volume 32π cubic centimeters. Quantity A Quantity B Radius of the base of the cone 6.25 centimeters

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume = (1/3) * pi * r^2 * h = 32pi. (1/3) * r^2 * 6 = 32. 2 * r^2 = 32. r^2 = 16. r = 4. Quantity A is 4, Quantity B is 6.25. So B is greater.

Multiple choice

Quantity A Height of a right circular cone with volume 12π cubic inches and radius 2 inches Quantity B Height of a right circular cone with volume 18π cubic inches and radius 3 inches

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume = (1/3) * pi * r^2 * h. For A: 12pi = (1/3) * pi * 2^2 * hA => 12 = (4/3) * hA => hA = 9. For B: 18pi = (1/3) * pi * 3^2 * hB => 18 = 3 * hB => hB = 6. Quantity A (9) > Quantity B (6).

Multiple choice

The area of the circle is divided into three sectors in the respective ratio of 3 : 4 : 5 and the area of the circle is 45π. Quantity A 3π Quantity B Area of the second smallest sector

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be established from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total ratio parts = 3+4+5 = 12. Total area = 45pi. One part = 45pi / 12 = 3.75pi. Sectors are 3*3.75pi = 11.25pi, 4*3.75pi = 15pi, 5*3.75pi = 18.75pi. The second smallest sector is 15pi. Quantity B (15pi) is greater than Quantity A (3pi).

Multiple choice

The height of a triangle ranges from 7 to 11 centimeters and the length of the base ranges from 4 centimeters to 9 centimeters. Quantity A The greatest possible area of the triangle Quantity B Area of a circle whose radius is 3 centimeters.

  1. Quantity A is greater.

  2. Quantity B is greater

  3. The two quantities are equal

  4. The relationship cannot be established from the information given
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The maximum area of a triangle is (1/2) * base * height. Using the maximum values (base=9, height=11), the area is 0.5 * 9 * 11 = 49.5. The area of a circle with radius 3 is pi * r^2 = 3.14 * 9 = 28.26. Since 49.5 > 28.26, Quantity A is greater.

Multiple choice

If the volume of sphere is 38,808 cm3 then find its radius?

  1. 15 cm

  2. 21 cm

  3. 14 cm

  4. 28 cm

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of a sphere is given by V = (4/3) * pi * r^3. Setting (4/3) * (22/7) * r^3 = 38808, we find r^3 = 38808 * 3 * 7 / (4 * 22) = 9261. Taking the cube root of 9261 gives r = 21 cm.