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 surface area of a solid hemisphere is
  1. $\pi { r }^{ 2 }$
  2. $4\pi { r }^{ 2 }$
  3. $\dfrac { 4 }{ 3 } \pi { r }^{ 2 }$
  4. $3\pi { r }^{ 2 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total surface area of a solid hemisphere includes the curved surface (2*pi*r^2) and the flat circular base (pi*r^2), totaling 3*pi*r^2.

Multiple choice

The inner curved surface area of a hemispherical dome of a building needs to be painted. If the circumference of the base is $17.6m$, find the cost of painting it at the rate of Rs.$5$ per sq.m
  1. Rs.$246.40$
  2. Rs.$24.40$
  3. Rs.$26.40$

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

Circumference of base = 2 * pi * r = 17.6. r = 17.6 / (2 * 3.14) = 2.8 m. Curved surface area of hemisphere = 2 * pi * r^2 = 2 * 3.14 * 2.8 * 2.8 = 49.28 sq.m. Cost = 49.28 * 5 = 246.40.

Multiple choice

Radius and slant height of a solid right circular cone are in the ratio $3:5$. If the curved surface area is $60\pi sq.cm$, then find its total surface area.
  1. $301\cfrac{5}{7}{cm}^{2}$
  2. $31\cfrac{5}{7}{cm}^{2}$
  3. $302\cfrac{5}{7}{cm}^{2}$

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

r/l = 3/5. Let r=3x, l=5x. h = sqrt(l^2 - r^2) = 4x. CSA = pi*r*l = pi*(3x)(5x) = 15*pi*x^2 = 60*pi. So x^2 = 4, x=2. r=6, l=10. TSA = pi*r(r+l) = pi*6*(6+10) = 96*pi = 96 * 3.14159 = 301.59. 301 5/7 is 301.71.

Multiple choice

The radius and height of a right circular cone are in th ratio $2:3$. Find the slant height if its volume is $100.48\ cm^3$. (Take $\pi =3.14$).
  1. $2\sqrt{13}cm$
  2. $4\sqrt{13}cm$
  3. $2\sqrt{3}cm$

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

Radius r = 2k, height h = 3k. Volume = (1/3) * pi * r^2 * h = (1/3) * 3.14 * (4k^2) * 3k = 12.56 * k^3 = 100.48. k^3 = 8, so k = 2. r = 4, h = 6. Slant height l = sqrt(r^2 + h^2) = sqrt(16 + 36) = sqrt(52) = 2 * sqrt(13).

Multiple choice

A lead pencil is in the shape of right circular cylinder. The pencil is $28cm$ long and its radius is $3mm$. If the lead is of radius $1mm$, then find the volume of the wood used in the pencil.
  1. $7.04{cm}^{3}$
  2. $7.14{cm}^{3}$
  3. $8.04{cm}^{3}$

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

The volume of the wood is the volume of the cylinder minus the volume of the lead core. Volume = pi * (R^2 - r^2) * h. With R = 0.3 cm, r = 0.1 cm, and h = 28 cm, Volume = pi * (0.09 - 0.01) * 28 = pi * 0.08 * 28 = 2.24 * 3.14159 = 7.037 cm^3, which rounds to 7.04 cm^3.

Multiple choice

Through a cylindrical pipe of internal radius $7cm$, water flows out at the rate of $5cm/sec$. Calculate the volume of water (in litres) discharged through pipe in half an hour.
  1. $1386$ litres
  2. $186$ litres
  3. $136$ litres

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

Volume = cross-sectional area * flow rate * time. Area = pi * r^2 = 22/7 * 7 * 7 = 154 cm^2. Flow rate = 5 cm/sec. Time = 30 min = 1800 sec. Volume = 154 * 5 * 1800 = 1,386,000 cm^3. Since 1000 cm^3 = 1 litre, volume = 1386 litres.

Multiple choice

The formula of lateral surface area of cylinder is ________.
  1. $A = 2\pi r h$
  2. $A = 2\pi r$
  3. $A = \pi r^{2}$
  4. $A = 2\pi r^{2}h$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The lateral surface area of a cylinder is the area of the side, which is the circumference of the base (2*pi*r) multiplied by the height (h). Thus, A = 2*pi*r*h.