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

A solid metal sphere is cut through the center into two equal parts Find the total surface area of each part it the radius of the sphere is 3.5 cm
  1. $\displaystyle 115.5cm^{2}$
  2. $\displaystyle 151.5cm^{2}$
  3. $\displaystyle 155cm^{2}$
  4. $\displaystyle 151cm^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A sphere cut in half creates two hemispheres. Each hemisphere has a curved surface area (2 * pi * r^2) and a flat circular base (pi * r^2). Total surface area = 3 * pi * r^2. r = 3.5. Area = 3 * (22/7) * 3.5 * 3.5 = 3 * 22 * 0.5 * 3.5 = 115.5.

Multiple choice

If the curved surface area and volume of a cylinder are $264 m^2$ and $924 m^3$ respectively, then the height of the cylinder is

  1. 6 m

  2. 6.5 m

  3. 6.7 m

  4. 6.8 m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Curved surface area (CSA) = 2 * pi * r * h = 264. Volume (V) = pi * r^2 * h = 924. Dividing V by CSA: (pi * r^2 * h) / (2 * pi * r * h) = 924 / 264. This simplifies to r / 2 = 3.5, so r = 7. Substitute r = 7 into CSA: 2 * (22/7) * 7 * h = 264, so 44 * h = 264, h = 6.

Multiple choice

A right circular cone and a cylinder have a circle of unit radius as base and their heights are equal to the radius itself and a hemisphere has the same radius then their volumes are proportional respectively to

  1. 1 : 2 : 3

  2. 3 : 2 : 1

  3. 2 : 1 : 3

  4. 1 : 3 : 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Cone: (1/3) * pi * r^2 * h = (1/3) * pi * 1^2 * 1 = pi/3. Cylinder: pi * r^2 * h = pi * 1^2 * 1 = pi. Hemisphere: (2/3) * pi * r^3 = (2/3) * pi * 1^3 = 2pi/3. Ratio: pi/3 : pi : 2pi/3 = 1 : 3 : 2.

Multiple choice

A cone hemisphere and a cylinder stands on equal bases and have the same height the height being equal to the radius of the circular base then their whole surface areas are in the ratio
  1. $ \displaystyle (\sqrt{2}+1):3:4 $
  2. $ \displaystyle (\sqrt{3}+1):3:4 $
  3. $ \displaystyle \sqrt{2}:3:4 $
  4. $ \displaystyle \sqrt{3}:7:8 $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

With radius r as the common height, the cone's whole surface area is (sqrt(2) + 1)pi r^2. The hemisphere and cylinder have whole surface areas 3pi r^2 and 4pi r^2, respectively. Their ratio is therefore (sqrt(2) + 1) : 3 : 4.

Multiple choice

The volume of the greatest sphere cut off from a cylindrical wood of base radius 1 cm and height 5 cm is
  1. $ \displaystyle \frac{4}{3}\times (5\pi )cm^{3} $
  2. $ \displaystyle \frac{4}{3} \pi cm^{3} $
  3. $ \displaystyle 5\pi cm^{3} $
  4. $ \displaystyle \frac{10\pi }{3}cm^{3} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The greatest sphere that can be cut from a cylinder of radius 1 cm and height 5 cm is limited by the radius. The sphere's radius is 1 cm. Volume = (4/3) * pi * r^3 = (4/3) * pi * 1^3 = (4/3) * pi.

Multiple choice

The total surface area of the cylindrical iron pillar surmounted by a cone of radius and height equal to that of the cylinder (r = 6 cm, h = 8 cm) is
  1. $ \displaystyle 190 \pi cm^{2} $
  2. $ \displaystyle 192 \pi cm^{2} $
  3. $ \displaystyle 195 \pi cm^{2} $
  4. $ \displaystyle 198 \pi cm^{2} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Surface area = Cylinder lateral area + Base area + Cone lateral area. Cylinder lateral = 2 * pi * r * h = 2 * pi * 6 * 8 = 96 pi. Base = pi * r^2 = 36 pi. Cone lateral = pi * r * l, where l = sqrt(r^2 + h^2) = 10. Cone lateral = pi * 6 * 10 = 60 pi. Total = 96 pi + 36 pi + 60 pi = 192 pi.

Multiple choice

The total surface area of a hemisphere of radius r is given by
  1. $ \displaystyle 2\pi r^{2} $
  2. $ \displaystyle \pi r^{2} $
  3. $ \displaystyle 3\pi r^{2} $
  4. $ \displaystyle 4\pi r^{2} $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A hemisphere has a curved surface area of 2*pi*r^2 and a flat circular base of pi*r^2. Total surface area = 3*pi*r^2.

Multiple choice

A cone of height 10 cm and radius 10 cm is to be divided into two parts by cutting through the mid point of the vertical axis Then the volume of the conical part is
  1. $ \displaystyle \frac{1000}{3}\pi cm^{3} $
  2. $ \displaystyle \frac{500}{3}\pi cm^{3} $
  3. $ \displaystyle \frac{250}{3}\pi cm^{3} $
  4. $ \displaystyle \frac{125}{3}\pi cm^{3} $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The cone is cut at the midpoint of the height. The smaller cone has height 5 and radius 5 (by similar triangles). Volume = (1/3) * pi * r^2 * h = (1/3) * pi * 5^2 * 5 = 125/3 * pi.