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

Quantity A The curved surface area of a cylinder with radius 3 units and height 7 units. Quantity B The curved surface area of a cone with radius 7 units and height 6 units.

  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

CSA Cylinder = 2 * pi * r * h = 2 * pi * 3 * 7 = 42 * pi. CSA Cone = pi * r * l. Slant height l = sqrt(r^2 + h^2) = sqrt(7^2 + 6^2) = sqrt(49 + 36) = sqrt(85) approx 9.22. CSA Cone = pi * 7 * 9.22 = 64.54 * pi. Since 64.54 > 42, Quantity B is greater.

Multiple choice

A cone is inscribed in a cylinder such that the base of the cone is equal to the base of the cylinder, and both have the same height. Additionally, the sum of the radius of the base of the cone and the height of the cone is 30 cm. If the total surface area of the cylinder (including both the top and bottom) is 1320 cm2, what is the total capacity (volume) of the cylinder in cubic centimeters?

  1. 1027π

  2. 1127π

  3. 1148π

  4. 1157π

  5. 1172π
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let r be radius, h be height. r + h = 30. Cylinder surface area = 2*pi*r^2 + 2*pi*r*h = 2*pi*r(r+h) = 1320. 2*pi*r(30) = 1320. r = 1320 / (60*pi) = 22/pi. This leads to h = 30 - 22/pi. The volume is pi*r^2*h. Calculation yields 1127pi.

Multiple choice

The radius and height of a cylinder are in the ratio 6 : 7 and its volume is 792 cm3. Calculate its curved surface area in cm2.

  1. 490

  2. 226

  3. 264

  4. 262
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let radius r = 6x and height h = 7x. Volume V = pi * r^2 * h = pi * (6x)^2 * (7x) = 252 * pi * x^3 = 792. Solving for x^3 gives x^3 = 792 / (252 * pi) approximately 1. Solving for x and then calculating curved surface area 2 * pi * r * h = 2 * pi * (6x) * (7x) = 84 * pi * x^2 yields 264.

Multiple choice

A soild trophy, consisting of two parts, has been designed in the following manner: the bottom part is a frustum of a cone with the bottom radius 30 cm, the top radius 20 cm, and height 40 cm, while the top part is a hemisphere with radius 20 cm. Moreover, the flat surface of the hemisphere is the same as the top surface of the frustum. If the entire trophy is to be gold-plated at the cost of Rs. 40 per square cm, what would the cost for gold plating be closest to?

  1. Rs. 1,12,000

  2. Rs. 3,60,000

  3. Rs. 4,73,000

  4. Rs. 5,23,000

  5. Rs. 3,72,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The surface area includes the lateral area of the frustum, the base of the frustum, and the curved surface of the hemisphere. Calculating these areas and multiplying by the cost per square cm yields approximately 473,000.

Multiple choice

Three solid cubes of metal have sides 6 cm, 8 cm and 10 cm, respectively. They are melted to form a new cube. What is the surface area of this new cube?

  1. 915 cm2

  2. 864 cm2

  3. 950 cm2

  4. 812 cm2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of the new cube is the sum of the volumes of the three smaller cubes: 6^3 + 8^3 + 10^3 = 216 + 512 + 1000 = 1728 cm^3. The side length of the new cube is the cube root of 1728, which is 12 cm. The surface area is 6 * (side^2) = 6 * 144 = 864 cm^2.

Multiple choice

A beverage company produces two models of cylindrical storage tanks. Each tank has a height of 60 centimeters. The radius of the smaller tank is 20 centimeters, while the radius of the larger tank is 20% greater than that of the smaller tank. What is the volume, in cubic centimeters, of the larger tank?

  1. 28,800π

  2. 30,000π

  3. 32,400π

  4. 34,560π
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The smaller tank radius is 20 cm. The larger tank radius is 20% greater, so 20 * 1.20 = 24 cm. The volume of a cylinder is pi * r^2 * h. For the larger tank, V = pi * 24^2 * 60 = pi * 576 * 60 = 34,560pi.

Multiple choice

A cylindrical storage jar has a base area of 90 square centimeters and a height of 12 centimeters. The jar contains layers of dry grains. When water is poured in, it takes 180 cubic centimeters of water to fill the jar to the top. Which of the following is closest to the total volume of the grains in the jar, in cubic centimeters?

  1. 90

  2. 270

  3. 900

  4. 1,080
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total volume of jar = Base Area * Height = 90 * 12 = 1080 cubic cm. Volume of grains = Total Volume - Volume of water = 1080 - 180 = 900 cubic cm.