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

The base radius of a cylinder is $1\dfrac {2}{3}$ times its height. The cost of painting its curved surface area at $2\ paise/ cm^{2}$ is Rs. $92.40$. Find the volume of the cylinder.
  1. $80850\ cm^{3}$
  2. $80580\ cm^{3}$
  3. $80508\ cm^{3}$
  4. $800508\ cm^{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Curved Surface Area (CSA) = Total Cost / Rate = 92.40 / 0.02 = 4620 cm^2. CSA = 2 * pi * r * h. Given r = 5/3 * h. 4620 = 2 * pi * (5/3 * h) * h. Solve for h, then find volume = pi * r^2 * h.

Multiple choice

What is the surface area of a cylinder that has a top and bottom if the height is $8.5$ units and the diameter is $3$ units?
  1. $18\pi$ square units
  2. $30\pi$ square units
  3. $32\pi$ square units
  4. $36\pi$ square units
  5. $54\pi$ square units
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Surface area of a cylinder = 2 * pi * r * h + 2 * pi * r^2. Diameter = 3, so radius r = 1.5. Height h = 8.5. Area = 2 * pi * 1.5 * 8.5 + 2 * pi * 1.5^2 = 25.5 * pi + 4.5 * pi = 30 * pi.

Multiple choice

A hollow cylinder having external radius $8$ cm and height $10$ cm has total surface area of $338$ $\pi cm^2$. Find the thickness of the hollow metallic cylinder.
  1. $2$ cm 
  2. $3$ cm
  3. $4$ cm
  4. $5$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total surface area of hollow cylinder = 2 * pi * (R+r) * (R-r+h) = 338 * pi. Given R=8, h=10. 2 * (8+r) * (8-r+10) = 338. (8+r)(18-r) = 169. 144 - 8r + 18r - r^2 = 169. r^2 - 10r + 25 = 0. (r-5)^2 = 0, r=5. Thickness = R - r = 8 - 5 = 3.