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 lateral surface area of a hollow cylinder is $5632 cm^{2}$. It is cut along its height and rectangular sheet of width $44 cm$ is formed. Find the perimeter of the rectangular sheet?
  1. $344 cm$
  2. $388 cm$
  3. $320 cm$
  4. $300 cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Lateral surface area = 2 * pi * r * h = 5632. When cut, it forms a rectangle with width 44. If width is height, h = 44. 2 * pi * r * 44 = 5632. 2 * pi * r = 128 (circumference). Perimeter of rectangle = 2 * (length + width) = 2 * (128 + 44) = 2 * 172 = 344.

Multiple choice

The area of the largest triangle that can be in-scribed in a semi circle whose radius is r cm is
  1. $ \displaystyle 2r$ $ \displaystyle cm^{2}$
  2. $ \displaystyle r^{2}$ $ \displaystyle cm^{2}$
  3. $ \displaystyle 2r^{2}$ $ \displaystyle cm^{2}$
  4. $ \displaystyle \frac{1}{4}r^{2}$ $ \displaystyle cm^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The base of the triangle is the diameter of the semicircle (2r) and the height is the radius (r). Area = (1/2) * base * height = (1/2) * 2r * r = r^2.

Multiple choice

The area of a circle which passes through the four vertices of a rectangle is $78.5$ $m^2$. One side of a rectangle is $6\ cm$. Find the other side or the rectangle ($\pi = 3.14$).
  1. $10\ cm$
  2. $8\ cm$
  3. $12\ cm$
  4. $4\ cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The circle through all four vertices of a rectangle has the rectangle's diagonal as its diameter. From the area, pi*r^2 = 78.5 gives r = 5, so the diameter (diagonal) is 10. With one side 6, the other side is sqrt(100 - 36) = 8.