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 hemispherical bowl is made from a metal sheet having thickness $0.3cm$. The inner radius of the bowl is $24.7cm$. Find the cost of polishing its outer surface at the rate of Rs.$4$ per $10{cm}^{2}$. (Take $\pi=3.14$)
  1. Rs.$1570$
  2. Rs.$137$
  3. Rs.$127$
  4. Rs.$107$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The outer radius is inner radius plus thickness, which is 24.7 + 0.3 = 25 cm. The outer surface area of a hemisphere is 2 * pi * r^2 = 2 * 3.14 * 25 * 25 = 3925 cm^2. At a rate of Rs 4 per 10 cm^2, the cost is (3925 / 10) * 4 = 392.5 * 4 = 1570.

Multiple choice

From a right circular cylinder with height $10\ cm$ and radius of base $6\ cm$, a right circular cone of the same height and base is removed. Find the volume of the remaining solid
  1. $754.28\ {cm}^{3}$
  2. $714.17\ {cm}^{3}$
  3. $654.18\ {cm}^{3}$
  4. $754.82\ {cm}^{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of cylinder = pi*r^2*h = pi*36*10 = 360*pi. Volume of cone = (1/3)*pi*r^2*h = 120*pi. Remaining volume = 240*pi. Using pi = 3.14159, 240*pi is approx 753.98, which is closest to 754.28.

Multiple choice

Three cylinders each of height $16$ cm and radius of base $4$ cm are placed on a plane, so that each cylinder touches the other two. Then the volume of region enclosed between the three cylinders in $cm^3$ is
  1. $98 (4\sqrt 3 - \pi)$
  2. $98 (2\sqrt 3 - \pi)$
  3. $98 (\sqrt 3 - \pi)$
  4. $128 (2\sqrt 3 - \pi)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The region enclosed between three cylinders of radius r forms an equilateral triangle of side 2r with three circular sectors of 60 degrees each. The area of the triangle is (sqrt(3)/4) * (2r)^2 = sqrt(3) * r^2, and the area of the three sectors is (3 * 60/360) * pi * r^2 = (1/2) * pi * r^2. The volume is height * (area of triangle - area of sectors) = 16 * (sqrt(3) * 16 - (pi * 16 / 2)) = 256 * sqrt(3) - 128 * pi = 128 * (2 * sqrt(3) - pi).

Multiple choice

The volume of a right circular cylinder can be obtained form its curved surface area by multiplying it by its
  1. $ \dfrac{Radius }{2}$
  2. $ \dfrac{2 }{Radius}$

  3. Height
  4. $2 \times$ height
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a right circular cylinder is given by pi * r^2 * h, and its curved surface area is 2 * pi * r * h. Dividing the volume by the curved surface area yields r / 2, which is half of the radius. Therefore, multiplying the curved surface area by Radius / 2 gives the volume.

Multiple choice

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq. cm) is
  1. 100 $\displaystyle \pi$
  2. 75 $\displaystyle \pi $
  3. 60 $\displaystyle \pi $
  4. 50 $\displaystyle \pi $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of the original sphere is (4/3) * pi * 10^3. When divided into 8 equal spheres, each small sphere has a volume of (1/8) * (4/3) * pi * 10^3 = (4/3) * pi * 5^3, meaning the radius of each small sphere is 5 cm. The surface area of each small sphere is 4 * pi * 5^2 = 100 * pi.

Multiple choice

A right circular cone has for its base a circle having the same radius as a given sphere. The volume of the cone is one-half that of the sphere. The ratio of the altitude of the cone to the radius of its base is
  1. $\displaystyle\frac{1}{1}$
  2. $\displaystyle\frac{1}{2}$
  3. $\displaystyle\frac{2}{1}$
  4. $\displaystyle\frac{2}{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let r be the radius of the sphere and the cone, and h be the height of the cone. The volume of the sphere is (4/3) * pi * r^3, and the volume of the cone is (1/3) * pi * r^2 * h. Given the cone volume is half the sphere volume, (1/3) * pi * r^2 * h = (1/2) * (4/3) * pi * r^3. Simplifying gives h = 2r, so the ratio h/r is 2/1.

Multiple choice

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is H cm and the diameter of the cylinder is 2 r cm. The volume of the solid is
  1. $\pi r^2\left (H-\dfrac {2r}{3}\right )cm^3$
  2. $\pi r^2\left (H+\dfrac {2r}{9}\right )cm^3$
  3. $\pi r^2\left (H-\dfrac {2r}{9}\right )cm^3$
  4. $\pi r\left (H-\dfrac {2r}{3}\right )cm^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The solid consists of a cylinder of height (H - 2r) and two hemispheres which form a sphere of radius r. Volume = pi * r^2 * (H - 2r) + (4/3) * pi * r^3 = pi * r^2 * (H - 2r + 4r/3) = pi * r^2 * (H - 2r/3).