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 area enclosed by the circumferences of two concentric circles is $346.5\, cm^2$. If the circumference of the inner circle is $88$ cm, then the radius of the outer circle is
  1. $88$ cm
  2. $17.5$ cm
  3. $35$ cm
  4. $9.3$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Circumference of inner circle = 2 * pi * r_inner = 88, so r_inner = 88 / (2 * pi) = 14 cm. Area difference = pi * (R^2 - r^2) = 346.5. R^2 - 14^2 = 346.5 / pi = 110.25. R^2 = 196 + 110.25 = 306.25. R = sqrt(306.25) = 17.5 cm.

Multiple choice

A cube of white chalk is painted red and then cut parallel to the sides to form two rectangular solids of equal volume. What percent of the surface area of each of the new solids in not painted red?
  1. $45$%
  2. $25$%
  3. $40$%
  4. $50$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cutting the painted cube into two equal cuboids exposes one new square face on each solid. Each cuboid has total surface area 4s^2, while the unpainted face has area s^2, giving 1/4 or 25%.

Multiple choice

Figure shows a metal ball suspended by thread of negligible mass from an upright cylinder that floats partially submerged in water. The cylinder has height 6 cm, face area $11 cm^2$ on the top and bottom and density $0.5 g/cm^3, 4 cm$ of cylinder's height is inside the water surface. If density of the metal ball is $8 gm/cm^3$ then its radius is equal to $\left(\dfrac{3}{x} \right)^{1/3}$ cm. calculate x. ($\rho_w = 1 gm/cm^3$)
  1. $7$
  2. $5$
  3. $3$
  4. $8$
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

We have a vessel in shape of a cuboid partially filled with water. Its base is square with an area of $4.5\ {dm}^{2} (1\ dm = 10\ cm)$ and the vessel contains water up to $2\ cm$ height. Then we place a wooden cube inside water. The wood has mass of $4\ kg$ and specific gravity $0.5$. The base of the wooden cube is horizontal. Find the height of water level above the base of the wooden block.
  1. $10\ cm$
  2. $5\ cm$
  3. $15\ cm$
  4. $7\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

A 700 g solid cube having an edge of length 10 cm floats in water. What volume of the cube is outside water ?
  1. $300 cm^3$
  2. $600 cm^3$
  3. $150 cm^3$
  4. $450 cm^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The cube floats, so the buoyant force equals the weight of the cube (700g). The volume of water displaced is 700 cm^3 (since density of water is 1g/cm^3). Total volume of the cube is 10*10*10 = 1000 cm^3. Volume outside water = Total volume - Displaced volume = 1000 - 700 = 300 cm^3.

Multiple choice

$\triangle ABC$ is a right triangle, the radius of its circumcircle is $3\ cm$ and the length of its altitude drawn from the opposite vertex to the hyptotenuse is $2\ cm$. Then the area of the triangle is
  1. $12\ sq. cm$
  2. $3\ sq. cm$
  3. $6\ sq. cm$
  4. $5\ sq. cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a right triangle, the hypotenuse is twice the circumradius, so its length is 6 cm. The area is 1/2 x hypotenuse x altitude to the hypotenuse = 1/2 x 6 x 2 = 6 square centimetres.