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

From a circle of radius $15\ cm$, a sector central angle $216^{o}$ is cut and its bounding radii are joined without overlap so as to form a cone. Find its volume.
  1. $1081.3\ cm^{3}$
  2. $1071.3\ cm^{3}$
  3. $1018.3\ cm^{3}$
  4. $1061.9\ cm^{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sector radius R=15, angle=216 degrees. Arc length = (216/360)*2*pi*15 = 18*pi. This becomes the circumference of the cone base: 2*pi*r = 18*pi, so r=9. Slant height l=15. Height h = sqrt(15^2 - 9^2) = 12. Volume = (1/3)*pi*r^2*h = (1/3)*pi*81*12 = 324*pi = 1017.87. 1018.3 is the closest approximation.

Multiple choice

STATEMENT - 1 : The volume of largest sphere that can be carved out from cube of side a cm is $\displaystyle \frac{1}{6} \pi a^3$ STATEMENT - 2 : Volume of sphere is $\displaystyle \frac{4}{3} \pi r^3$ and for largest sphere to carved from cube radius of sphere $=$ side of cube

  1. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

  2. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

  3. Statement - 1 is True, Statement - 2 is False

  4. Statement - 1 is False, Statement - 2 is True
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

The total surface area of a solid cylinder is $462{cm}^{2}$. Its curved surface area is one third of total surface area. Find the volume of the cylinder.
  1. $229\ cm^3$
  2. $509\ cm^3$
  3. $439\ cm^3$
  4. $539\ cm^3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

TSA = 462, CSA = 1/3 * 462 = 154. TSA = CSA + 2 * pi * r^2, so 462 = 154 + 2 * pi * r^2 => 2 * pi * r^2 = 308 => r^2 = 308 * 7 / 44 = 49 => r = 7. CSA = 2 * pi * r * h = 154 => 2 * (22/7) * 7 * h = 154 => 44h = 154 => h = 3.5. Volume = pi * r^2 * h = (22/7) * 49 * 3.5 = 22 * 7 * 3.5 = 539.

Multiple choice

The height of the cylinder of mas.Volume that can be inscribed in a sphere of radius $\alpha$ is
  1. $\dfrac{2\alpha}{\sqrt{3}}$
  2. $\dfrac{\alpha}{\sqrt{2}}$
  3. $\dfrac{5\alpha}{4}$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a cylinder inscribed in a sphere of radius a, the volume is V = pi * r^2 * h. Since r^2 + (h/2)^2 = a^2, V = pi * (a^2 - h^2/4) * h = pi * (a^2 * h - h^3/4). Differentiating with respect to h and setting to zero gives a^2 - 3h^2/4 = 0, so h^2 = 4a^2/3, h = 2a / sqrt(3).