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

What will be the total surface area of the given cylinder? (A) Volume of cone having height 21 cm is equal to 1078 cm3 and area of base of cone is ¼ of area of base of cylinder. (B) Ratio of height and diameter of given cylinder is 3:4. (C) Height is 7 cm more than radius of cylinder

  1. Either A or B and C together

  2. Either A and B or B and C

  3. Any two of them

  4. Any one of them

  5. Either A and B or A and C
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement A determines the cylinder's radius through the base-area relationship and cone volume. Statements B and C together determine the radius and height directly, while A with either B or C also supplies enough information. Thus any two statements are sufficient.

Multiple choice

Directions: Each question is followed by three statements. You have to study the question and all the three statements given and decide whether any information provided in the statement(s) is redundant and can be dispensed with while answering the questions. What is the area of the rectangle? A. Perimeter of the rectangle is 80 m. B. The total cost of flooring the rectangle at Rs. 2 per square metre is Rs. 750. C. Breadth of the rectangle is 15 m.

  1. Only B

  2. A and B together

  3. Either B alone or A and C together

  4. None

  5. A and C together
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area = L * B. A (Perimeter) gives 2(L+B) = 80, so L+B = 40. B (Cost) gives Area * 2 = 750, so Area = 375. C gives B = 15. To find Area, we need L and B. B alone gives the area directly. A and C together give L+15=40, so L=25, and Area=25*15=375. Thus, either B alone or A and C together are sufficient.

Multiple choice

Find the area of circle whose diameter is 56cm

  1. 2434cm2

  2. 4264cm2

  3. 2464cm2

  4. 6664cm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The diameter is 56 cm, so the radius r = 28 cm. The area of a circle is pi * r^2. Using pi = 22/7, area = (22/7) * 28 * 28 = 22 * 4 * 28 = 88 * 28 = 2464 cm^2.

Multiple choice

A cup is in the form of a hemisphere surmounted by a cylinder. The height of the cylindrical portion is 9 cm and the total height of the cup is 12.5 cm. Then the radius of the cylindrical portion is

  1. 3.5 cm

  2. 2.5cm

  3. 21.5cm

  4. 9 cm

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

The total height of the cup is the sum of the cylinder height and the hemisphere radius. Since the total height is 12.5 cm and the cylinder height is 9 cm, the radius is 12.5 - 9 = 3.5 cm.

Multiple choice

The height of a right circular cone is 35 cm and the area of its curved surface is four times the area of its base. What is the volume of the cone (in 10-3 m3 and correct up to three decimal places)?

  1. 3.316

  2. 3.384

  3. 2.994

  4. 2.625
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Curved surface area = pi * r * l = 4 * (pi * r^2) => l = 4r. l^2 = r^2 + h^2 => (4r)^2 = r^2 + 35^2 => 15r^2 = 1225 => r^2 = 81.66 => r = 9.037. Volume = (1/3) * pi * r^2 * h = (1/3) * pi * 81.66 * 35 = 2994.4 cm^3 = 2.994 * 10^-3 m^3.

Multiple choice

The sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m, The side length of one of these square is _____.

  1. 10 m

  2. 11 m

  3. 12 m

  4. 13 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let sides be x and y. x^2 + y^2 = 468 and 4x - 4y = 24 (so x - y = 6). Substituting y = x - 6 into the first equation gives x^2 + (x-6)^2 = 468, which simplifies to 2x^2 - 12x - 432 = 0, or x^2 - 6x - 216 = 0. Factoring gives (x-18)(x+12) = 0, so x = 18 and y = 12.

Multiple choice

[CAT 1994] A right circular cone, a right circular cylinder and a hemisphere, all have the same radius, and the heights of the cone and cylinder equal to their diameters. Then their volumes are proportional, respectively to

  1. 1:3:1

  2. 2:1:3

  3. 3:2:1

  4. 1:2:3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Radius r, height h. Cone: h=2r, V = 1/3 * pi * r^2 * (2r) = 2/3 * pi * r^3. Cylinder: h=2r, V = pi * r^2 * (2r) = 2 * pi * r^3. Hemisphere: V = 2/3 * pi * r^3. Ratio: (2/3) : 2 : (2/3) = 1 : 3 : 1.