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 curved surface area of a hemisphere is $\displaystyle 905! \frac{1}{7}! \ \text{cm}^2$, what is its volume?
  1. $3580.57 \,\text{cm}^3$
  2. $8220.57 \,\text{cm}^3$
  3. $8830.57 \,\text{cm}^3$
  4. $3620.57 \,\text{cm}^3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The curved surface area of a hemisphere is 2*pi*r^2 = 6337/7. Solving for r^2 gives r^2 = 6337 / (14 * pi) approx 144, so r = 12. The volume is (2/3)*pi*r^3 = (2/3)*pi*1728 = 1152*pi, which is approximately 3619.11. Option D is the closest value.

Multiple choice

The radius of a solid right circular cylinder decreases by $20\%$ and its height increases by $10\%$. Find the percentage change in its curved surface area
  1. Decrease $ =$ $19\%$
  2. Decrease $ =$ $12\%$
  3. Decrease $ =$ $15\%$
  4. Decrease $ =$ $13\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Curved surface area S = 2 * pi * r * h. If r decreases by 20% (new r = 0.8r) and h increases by 10% (new h = 1.1h), the new area S' = 2 * pi * (0.8r) * (1.1h) = 0.88 * (2 * pi * r * h) = 0.88S. This represents a 12% decrease.

Multiple choice

The diameter of the base of metallic cone is $2$ cm and height is $10$ cm. $900$ such cones are molten to form 1 right circular cylinder whose radius is $10$ cm. Find total surface area of the right circular cylinder so formed. (Given $\pi$ = 3.14)
  1. $2510$ c$m^2$
  2. $2512$ $cm^2$
  3. $2515$ $cm^2$
  4. $2530$ $cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of 900 cones = 900 * (1/3 * pi * 1^2 * 10) = 3000 * pi. Cylinder volume = pi * 10^2 * h = 100 * pi * h. So h = 30. Total surface area = 2 * pi * r * (h + r) = 2 * 3.14 * 10 * (30 + 10) = 2512.

Multiple choice

The length, breadth and height of a cuboid are in the ratio $5:4:2$. If the total surface area is $1216$ c$m^2$, find the dimensions of the solid.
  1. $(21 \times 11 \times 8) $ cm
  2. $(20 \times 16 \times 8)$  cm
  3. $(27 \times 17 \times 8) $ cm
  4. $(25 \times 19 \times 8)$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Dimensions are 5x, 4x, 2x. TSA = 2(lw + lh + wh) = 2(20x^2 + 10x^2 + 8x^2) = 2(38x^2) = 76x^2. 76x^2 = 1216. x^2 = 16, so x = 4. Dimensions are 20, 16, 8.

Multiple choice

The difference between the outer and the inner curved surface areas of an open cylinder is $88:cm^{2}$. If its length is $14$ cm and volume of the material in it is $176:cm^{3}$, find the inner diameter of the cylinder.
  1. $3$ cm
  2. $4 $ cm
  3. $2 $ cm
  4. $1 $ cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let R be outer radius, r be inner radius, h=14. Difference in CSA = 2*pi*h*(R-r) = 88. 2*(22/7)14(R-r) = 88. 88*(R-r) = 88, so R-r = 1. Volume = pi*h*(R^2-r^2) = 176. (22/7)14(R-r)(R+r) = 176. 44*1*(R+r) = 176, so R+r = 4. Solving R-r=1 and R+r=4 gives 2R=5, 2r=3. Inner diameter = 2r = 3.

Multiple choice

A rectangle plot of land measures $45$ m $\times$ $30$ m. A boundary wall of height $2.4$ m is built all round the plot at a distance of $1$ m from the plot. Find the area of the inner surface of the boundary wall.
  1. $226.2m^{2}$
  2. $457.2m^{2}$
  3. $379.2m^{2}$
  4. $291.2m^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The wall is 1m from the plot, so the dimensions of the wall perimeter are (45+2) and (30+2) = 47m and 32m. Perimeter = 2 * (47 + 32) = 158m. Area of inner surface = Perimeter * height = 158 * 2.4 = 379.2.

Multiple choice

The height and the radius of the base of a cylinder are in the ratio $3:1$. If its volume is $1029$ $ \pi\, cm^{3}$; find its total surface area.
  1. $1232$ $cm^{2}$
  2. $1200$ $cm^2$
  3. $1230$ $cm^2$
  4. $1233$ $cm^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given h/r = 3/1, so h = 3r. Volume = pi * r^2 * h = pi * r^2 * (3r) = 3 * pi * r^3 = 1029 * pi. Thus r^3 = 343, so r = 7 and h = 21. Total surface area = 2 * pi * r * (r + h) = 2 * pi * 7 * (7 + 21) = 14 * pi * 28 = 392 * pi. Using pi = 22/7, area = 392 * (22/7) = 56 * 22 = 1232.