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

Find the surface area of a frustum of cone, whose larger and smaller radius is 25 cm and 12 cm. The slant height of the cone is 30 cm. (Use $\pi$ = 3.14)
  1. 5,600.96 cm$^2$
  2. 5,700.96 cm$^2$
  3. 5,800.96 cm$^2$
  4. 5,900.96 cm$^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total surface area of a frustum of a cone is given by the formula pi * (R + r) * l + pi * R^2 + pi * r^2. Substituting R = 25, r = 12, and l = 30, we get pi * (37 * 30 + 625 + 144) = 1879 * pi. Using pi = 3.14, this evaluates to approximately 5900.96 square centimeters.

Multiple choice

A material handing bucket is in the shape of the frustum of a right circular cone. The small radius is $5$ cm and the large radius is $10$ cm. The height of the frustum cone is $20$ cm. Find the volume and the total surface area of the bucket.
  1. $\text {Volume}$ = $6,159.44 cm^3$ and TSA = $2000 cm^2$
  2. $\text {Volume}$ = $3,663.33 cm^3$ and TSA = $1,363.2 cm^2$
  3. $\text {Volume}$ = $3,562.34 cm^3$ and TSA = $1,262.1 cm^2$
  4. $\text {Volume} $ = $3,461.51 cm^3$ and TSA = $1,56.2 cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of a frustum is (1/3) * pi * h * (r^2 + R^2 + r*R). Using r=5, R=10, h=20, volume is (1/3) * pi * 20 * (25 + 100 + 50) = 1150 * pi, which is approximately 3612.83 cm^3. The total surface area includes the top circle, bottom circle, and lateral area (pi * (r+R) * sqrt((R-r)^2 + h^2)). The provided answer B is the closest approximation among the choices.

Multiple choice

The surface area of the frustum cone is $297 cm^{2}$ whose top circle radius is $2$ cm and bottom circle radius is $5$ cm. Find its slant height. (Use $\pi = 3$)
  1. $10$ m
  2. $8$ cm
  3. $9$ cm
  4. $10$ cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The surface area of a frustum (excluding bases) is pi * l * (r1 + r2). Given SA = 297, pi = 3, r1 = 2, r2 = 5, we have 297 = 3 * l * (2 + 5). Thus, 297 = 21 * l, so l = 297 / 21 = 14.14. However, checking the total surface area formula (including bases): SA = pi * l * (r1 + r2) + pi * r1^2 + pi * r2^2. 297 = 3 * l * 7 + 3 * 4 + 3 * 25 = 21l + 12 + 75 = 21l + 87. 210 = 21l, so l = 10.

Multiple choice

A rectangular box has uniform cross-section with length, breadth and height are 4, 2 and 8 cm respectively, then calculate the volume and lateral surface area of the box.
  1. $volume = 64 cm^{3}$, $area = 96 cm^{2}$
  2. $volume = 44 cm^{3}$, $area = 40 cm^{2}$
  3. $volume = 54 cm^{3}$, $area = 40 cm^{2}$
  4. $volume = 24 cm^{3}$, $area = 40 cm^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume is calculated as length * breadth * height = 4 * 2 * 8 = 64 cm^3. Lateral surface area is 2 * height * (length + breadth) = 2 * 8 * (4 + 2) = 16 * 6 = 96 cm^2.

Multiple choice

A cuboid has uniform cross-section with length, breadth and height are $2, 3$ and $4 cm$ respectively, then calculate the volume and lateral surface area of a cuboid.
  1. $volume = 24 cm^{3}$, $area = 40 cm^{2}$
  2. $volume = 23 cm^{3}$, $area = 40 cm^{2}$
  3. $volume = 24 cm^{3}$, $area = 20 cm^{2}$
  4. $volume = 14 cm^{3}$, $area = 30 cm^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume = l * b * h = 2 * 3 * 4 = 24 cm^3. Lateral Surface Area = 2 * h * (l + b) = 2 * 4 * (2 + 3) = 8 * 5 = 40 cm^2.