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 triangle with sides 3 cm, 4 cm and 5 cm is revolved about the side 3cm to form a cone. Which of these is false?

  1. Curved surface of cone =20π

  2. Total surface area = 36π

  3. Volume=(80 /3)π

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Revolving a 3-4-5 triangle about the 3cm side creates a cone with height h=3, radius r=4, and slant height l=5. Curved surface area = pi*r*l = pi*4*5 = 20*pi. Total surface area = pi*r*l + pi*r^2 = 20*pi + 16*pi = 36*pi. Volume = (1/3)*pi*r^2*h = (1/3)*pi*16*3 = 16*pi. Option C claims volume is 80/3*pi, which is false.

Multiple choice

A and B are two metallic solid spheres such that the surface area of B is 800% more than that of A. If the volume of A is x% less than that of B, then the value of x is closest to

  1. 64.2

  2. 72.4

  3. 95.5

  4. 96.3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Surface area of a sphere is proportional to r^2. If area of B is 800% more than A, then Area(B) = 9 * Area(A), so r(B) = 3 * r(A). Volume is proportional to r^3, so Volume(B) = 27 * Volume(A). Thus, A is 26/27 of B smaller, which is approximately 96.3%.

Multiple choice

The curved surface area of a cylinder is five times the area of its base. Find the ratio of the radius and height of the cylinder.

  1. 2 : 3

  2. 3 : 5

  3. 2 : 5

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

The curved surface area of a cylinder is given by 2 * pi * r * h, and the area of its base is pi * r^2. Setting the curved surface area equal to five times the base area gives 2 * pi * r * h = 5 * pi * r^2, which simplifies to 2h = 5r. Rearranging this equation to find the ratio of radius to height (r/h) yields 2/5, or 2 : 5.

Multiple choice

How many liters of water are required to completely fill the cylindrical tank of inner radius 4 inch? (1) The curved surface area from the out side of the tank is 80 square inch. (2) The depth of the tank is 10 inch.

  1. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

A square is inscribed within a circle of radius 10 centimeters. Use 3.14 for the value of π. Quantity A Area of the circle that is not covered by the square Quantity B 30 square 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 given data.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Circle area = pi * r^2 = 3.14 * 100 = 314. Square inscribed in circle has diagonal = 2r = 20. Side s = 20/sqrt(2) = 10*sqrt(2). Square area = s^2 = 200. Area not covered = 314 - 200 = 114. 114 > 30.