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 military of height $8.25\ m$ is in the form of a right circular cylinder of base diameter $30\ m$ and height $5.5\ m$ surmounted by a right circular cone of same base radius. Find the length of the canvas use in making the tent, if the breadth of the canvas is $1.5\ m$
  1. $500.26$m
  2. $224.26$m
  3. $824.26$m
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The cone has vertical height 2.75 m and radius 15 m, so its slant height is 15.25 m. The canvas area is pi*15.25*15 + 2pi*15*5.5, and dividing by the canvas breadth 1.5 m gives approximately 824.26 m.

Multiple choice

A piece of paper in the shape of a sector of a circle of radius 10cm and of angle $\displaystyle 216^{\circ}$ just covers the lateral surface of a right circular cone of vertical angle$\displaystyle 2\theta$ .Then $\displaystyle \sin: \theta$ is
  1. $\displaystyle \frac{3}{5}$
  2. $\displaystyle \frac{4}{5}$
  3. $\displaystyle \frac{3}{4}$

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sector radius R = 10, angle = 216 degrees. Arc length = (216/360) * 2 * pi * 10 = 12 * pi. This arc becomes the circumference of the cone base: 2 * pi * r = 12 * pi, so r = 6. Slant height l = 10. sin(theta) = r / l = 6 / 10 = 3/5.

Multiple choice

The area of circle with radius $24$cm is
  1. $576\pi $
  2. $24\pi$
  3. $12\pi$
  4. $48\pi$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a circle is calculated using the formula Area = pi * r^2. With a radius of 24 cm, the area is pi * (24)^2 = 576 * pi.

Multiple choice

The circumference of a circle is 123.2 cm. Taking $\pi \, =\, \displaystyle \frac{22}{7}$, calculate the area of the circle in $cm^2$, correct to the nearest $cm^2$ is
  1. $196\, cm^2$
  2. $1207\, cm^2$
  3. $2414\, cm^2$
  4. $2207\, cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Circumference = 2 * pi * r = 123.2. r = 123.2 / (2 * 22/7) = 123.2 * 7 / 44 = 19.6. Area = pi * r^2 = (22/7) * 19.6 * 19.6 = 22 * 2.8 * 19.6 = 1207.36. Rounded to the nearest integer, it is 1207.