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

Three circles each of radius $3.5$ cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.
  1. $ 3.932\ cm^{ 2 } $
  2. $ 19.251\ cm^{ 2 } $
  3. $ 21.217\ cm^{ 2 } $
  4. $ 1.966\ cm^{ 2 } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Three circles of radius r=3.5 form an equilateral triangle of side 2r=7. Area of triangle = (sqrt(3)/4) * side^2 = (1.732/4) * 49 = 21.217. Area of three sectors (each 60 degrees) = 3 * (60/360) * pi * r^2 = 0.5 * 3.14 * 12.25 = 19.2325. Enclosed area = 21.217 - 19.2325 = 1.9845. The closest option is 1.966.

Multiple choice

The ratio between curved surface area and total surface area of a cylinder is $2\,\colon\,3$. If the total surface area be $924\;cm^2$, find the volume of the cylinder.
  1. $2156\;cm^3$
  2. $1256\;cm^3$
  3. $1265\;cm^3$
  4. $1862\;cm^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

CSA/TSA = 2pi*r*h / (2pi*r*h + 2pi*r^2) = h / (h+r) = 2/3. So 3h = 2h + 2r, h = 2r. TSA = 2pi*r(h+r) = 2pi*r(3r) = 6pi*r^2 = 924. pi*r^2 = 154. r^2 = 154 * 7/22 = 49, r = 7. h = 14. Volume = pi*r^2*h = (22/7) * 49 * 14 = 22 * 7 * 14 = 2156.

Multiple choice

The diameters of external and internal surfaces of a hollow spherical shell are 10 cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of $2\dfrac {2}{3}cm$, find the diameter of the cylinder in cm
  1. $14$
  2. $16$
  3. $18$
  4. $20$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of hollow sphere = (4/3) * pi * (R^3 - r^3) = (4/3) * pi * (5^3 - 3^3) = (4/3) * pi * (125 - 27) = (4/3) * pi * 98 = 392/3 * pi. Cylinder volume = pi * r_c^2 * h = pi * r_c^2 * (8/3). Setting equal: 392/3 * pi = 8/3 * pi * r_c^2, so r_c^2 = 392/8 = 49. Radius = 7, diameter = 14.

Multiple choice

The volume of a cylinder is $\displaystyle 448\pi : cm^{3}$ and height is $7$ cm The lateral surface area of cylinder is
  1. $252$ $\displaystyle cm^{2}$
  2. $300$ $\displaystyle cm^{2}$
  3. $352$ $\displaystyle cm^{2}$
  4. $400$ $\displaystyle cm^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume V = pi * r^2 * h = 448pi. With h=7, r^2 = 448/7 = 64, so r = 8. Lateral surface area = 2 * pi * r * h = 2 * pi * 8 * 7 = 112pi. 112 * 3.14159 = 351.85, which is 352.