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

If $ \displaystyle S_{1} $ and $\displaystyle S_{2} $ be the whole surface of a sphere and the curved surface of the circumscribed cylinder then $ \displaystyle S_{1} $ is equal to
  1. $ \displaystyle S_{2} $
  2. $ \displaystyle 2S_{2} $
  3. $ \displaystyle \frac{1}{2}S_{2} $
  4. $ \displaystyle \frac{2}{3}S_{2} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Surface area of sphere S1 = 4*pi*r^2. Circumscribed cylinder has height h = 2r and radius r. Curved surface area S2 = 2*pi*r*h = 2*pi*r*(2r) = 4*pi*r^2. Thus S1 = S2.

Multiple choice

The total surface area of a metallic hemisphere is $1848\ cm^{2}$. The hemisphere is melted to form a solid right circular cone. If the radius of the base of the cone is the same as the radius of the hemisphere, its height is
  1. $42\ cm$
  2. $26\ cm$
  3. $28\ cm$
  4. $30\ cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

TSA of hemisphere = 3 * pi * r^2 = 1848. r^2 = 1848 / (3 * 22/7) = 1848 * 7 / 66 = 196. r = 14. Volume of hemisphere = 2/3 * pi * r^3 = 2/3 * 22/7 * 14^3 = 5749.33. Volume of cone = 1/3 * pi * r^2 * h = 1/3 * 22/7 * 14^2 * h = 5749.33. 1/3 * 22/7 * 196 * h = 5749.33. h = 28.

Multiple choice

The length, breadth and height of a rectangular solid are in the ratio $5: 4: 2$. If the total surface area is $1216\ cm^2,$ find the length, the breadth and the height of the solid.
  1. $20cm, 16cm$ and $ 8 cm$  
  2. $10cm, 16cm$ and $ 8 cm$  
  3. $10cm, 8cm$ and $ 2 cm$  
  4. $15cm, 12cm$ and $ 6cm$  
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let dimensions be 5x, 4x, 2x. Surface area = 2(5x*4x + 4x*2x + 5x*2x) = 2(20x^2 + 8x^2 + 10x^2) = 2(38x^2) = 76x^2. 76x^2 = 1216, so x^2 = 16, x = 4. Dimensions are 20, 16, 8.

Multiple choice

The area of the base of a rectangle tank is $6500c{m^2}$ and the volume of water contained in it is $2.6$ cubic metres. The depth of water in the tank is:

  1. 3.5m

  2. 4m

  3. 5m

  4. 6m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume is equal to base area multiplied by height. Converting 2.6 cubic meters to 26000 cubic centimeters, the height is 26000 / 6500 = 4 cm. Note that the options are in meters, implying the question likely intended 2.6 cubic meters and 6500 square centimeters, resulting in 4 meters.

Multiple choice

The volume of a rectangle block of stone is $10368d{m^3}$. Its dimensions are in the ratio $3:2:1$. If its entire surface is polished at $2$ paise per $d{m^2}$, then the total cost will be
  1. $Rs \ 31.50$
  2. $Rs \ 31.68$
  3. $Rs \ 63$
  4. $Rs \ 63.36$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the dimensions be 3x, 2x, and x. Since 6x^3 = 10,368, x = 12 dm, giving dimensions 36 dm, 24 dm, and 12 dm. The total surface area is 3,168 dm^2, and at 2 paise per dm^2 the cost is Rs. 63.36.

Multiple choice

The dimensions of a solid metal cuboid are $\displaystyle 72cm\times 30cm\times 75cm.$ It is melted and recast into indentical solid metal cubes with edge of each 6 cm. Find the number of cubes formed. Also, find the cost of polishing the surfaces of all cubes formed at the rate Rs. 150 per sq. m.
  1. $710$; Rs.$ 2,430$
  2. $790$; Rs. $2,430$
  3. $740$; Rs.$ 2,430$
  4. $750$; Rs. $2,430$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Number of cubes = (72*30*75) / (6^3) = 162000 / 216 = 750. Surface area of one cube = 6 * 6^2 = 216 cm^2 = 0.0216 m^2. Total surface area = 750 * 0.0216 = 16.2 m^2. Cost = 16.2 * 150 = 2430.