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 slant height of a cone whose, Base radius $=14\;cm$, height $0.48\;m$ Base diameter $=70\;cm$, curved surface area $=4070\;cm^2$
  1. $52\;cm\;;\;37\;cm$
  2. $50\;cm\;;\;37\;cm$
  3. $51\;cm\;;\;37\;cm$
  4. $50\;cm\;;\;36\;cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The prompt combines two cone datasets. For radius 14 cm and height 48 cm, the slant height is sqrt(14^2 + 48^2) = 50 cm. For diameter 70 cm and curved surface area 4070 cm^2, the slant height is 37 cm, so the paired answer is B.

Multiple choice

A metal cylinder with height $10\;cm$ and the diameter of base $70\;cm$ is melted to make a number of small discs with radius $1\;cm$ and thickness $0.5\;cm$. How many such discs could be made from the cylinder?
  1. $24400$ discs.
  2. $23500$ discs.
  3. $24500$ discs.
  4. $22500$ discs.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * (35)^2 * 10 = 12250 * pi. Volume of one disc = pi * (1)^2 * 0.5 = 0.5 * pi. Number of discs = (12250 * pi) / (0.5 * pi) = 24500.

Multiple choice

Find the volume of a sphere of radius $2.1\;cm$.
  1. $34.8\;cm^3$
  2. $35.8\;cm^3$
  3. $38.8\;cm^3$
  4. $36.8\;cm^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a sphere is (4/3) * pi * r^3. With r = 2.1, V = (4/3) * 3.14159 * (2.1)^3 = (4/3) * 3.14159 * 9.261 = 38.792 cm^3, which rounds to 38.8 cm^3.

Multiple choice

A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and slant height of the conical portion is 53 m, find the area of the canvas needed to make the tent

  1. 9735

  2. 9730

  3. 9720

  4. 9710
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Canvas area = lateral area of cylinder + lateral area of cone. Cylinder lateral area = 2 * pi * r * h = 2 * (22/7) * 52.5 * 3 = 990. Cone lateral area = pi * r * l = (22/7) * 52.5 * 53 = 8745. Total = 990 + 8745 = 9735.

Multiple choice

The radius of a sphere is 3 cm its volume is
  1. 113.14 $\displaystyle cm^{3}$
  2. 120 $\displaystyle cm^{3}$
  3. 108 $\displaystyle cm^{3}$
  4. 112.12 $\displaystyle cm^{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of a sphere = (4/3) * pi * r^3. With r = 3, V = (4/3) * 3.14 * 27 = 4 * 3.14 * 9 = 113.04. Option A is the closest.

Multiple choice

A right triangle with its sides $9\space cm, 12\space cm$ and $15\space cm$ is revolved about the side $12\space cm$. Find the volume of the solid so formed.
  1. $1018.28\space cm^3$
  2. $702.57\space cm^3$
  3. $652.57\space cm^3$
  4. $752.57\space cm^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Revolving a right triangle around one of its legs creates a cone. The leg it revolves around is the height (h=12), and the other leg is the radius (r=9). Volume = (1/3) * pi * r^2 * h = (1/3) * 3.14159 * 81 * 12 = 1017.876. The option 1018.28 is the closest approximation using a slightly different pi value.