Quantitative Aptitude

Mensuration of Solid Figures

147 Questions

Mensuration of solid figures deals with calculating the volume and surface area of 3D shapes. Common structures include cubes, cuboids, and rectangular prisms. These quantitative aptitude questions are standard in SSC, banking, and railway recruitment tests.

Cube volume formulasCuboid surface areaRectangular prismsDensity calculationsDimensional ratios

Mensuration of Solid Figures Questions

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are 4% and 3% respectively, the maximum error in the measurement of the density is

  1. 9%

  2. 13%

  3. 12%

  4. 7%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$Density, \rho = \dfrac{Mass}{Volume}=\dfrac{M}{L^3}$
Thus, maximum error, $\dfrac{\Delta \rho}{\rho}=\dfrac{\Delta M}{M}+3\dfrac{\Delta L}{L}=0.04+3\times 0.03$$= 0.13$ or $13\%$

Multiple choice physics units and measurement: error analysis rounding off digits rounding of digits standard form

A cube has a side of length 1.2 x $10^{-2}$. Its volume upto correct significant figures is

  1. 1.7 x $10^{-6}m^3$
  2. 1.73 x $10^{-6}m^3$
  3. 1.78 x $10^{-6}m^3$
  4. 1.732 x $10^{-6}m^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Here
Length of the cube, $L =12 x10^{-2} m$
Volume of the cube, $V= (1.2 \times10^{-2} m)^3= 1.728 \times 10^{-6}m^3$
As the result can have only two significant figures, therefore, on rounding off, we get, $V. 1.7 \times 10^{-6} m^3$
Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The edge of a cube is a $=1.2\times 10^{-2}m$. Then its volume will be recorded as :

  1. $1.7\times 10^{-6} m^3$
  2. $1.70\times 10^{-6} m^3$
  3. $1.70\times 10^{-7} m^3$
  4. $1.78\times 10^{-6} m^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given that the edge of a cube is  $a=1.2 \times 10^{-2}m$.
The volume of a cube $= a^{3}$.
Volume $=[1.2 \times 10^{-2} ]^{3}$
The given volume of the cube is $1.728 \times 10^{-6}m^{3}$ 

$ \approx 1.7 \times 10^{-6}m^{3} \ \ \ (upto \ two \  significant  \ digits)$

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The length, breadth and thickness of a block are given by $l = 12\  cm$, $b = 6\  cm$ and $t = 2.45 cm$. The volume of the block according to the idea of significant figures should be :

  1. $\displaystyle 1\times 10^{2}\:cm^{3}$
  2. $\displaystyle 2\times 10^{2}\:cm^{3}$
  3. $\displaystyle 1.763\times 10^{2}\:cm^{3}$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since question contains atleast 1 significant number in one of the value, therefore, we should write the answer in such a form that it contains only one significant figure. $V=lbt=12\times 6\times 2.45=2\times 10^2\ cm^3$

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

Length, breadth and thickness of a rectangular slab are 4.234 m, 1.005 m and 2.01 m respectively. Find volume of the slab to correct significant figures.

  1. $\displaystyle 8.55 m^{3}$
  2. $\displaystyle 8.552 m^{3}$
  3. $\displaystyle 8.6 m^{3}$

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

l = 4.234 m 4 significant figures

b = 1.005 m 4 significant figures
w = 2.01 m 3 significant figures 
Therefore, Volume = lbw= 8.55 .........3 significant figures

Multiple choice

What is the volume of a rectangular prism with length 8, width 5, and height 3?

  1. 120

  2. 150

  3. 180

  4. 210
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a rectangular prism with length l, width w, and height h is given by the formula (V = lwh). Substituting l = 8, w = 5, and h = 3 into the formula, we get: (V = 8 \cdot 5 \cdot 3 = 120). Therefore, the volume of the rectangular prism is 120.

Multiple choice

What is the volume of a cube with side length 3?

  1. 9

  2. 18

  3. 27

  4. 36
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a cube is given by the formula s^3. Substituting s = 3, we get 3^3 = 27.

Multiple choice

The volume of a cube is given by the formula:

  1. V = s^3

  2. V = s^2

  3. V = s * h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cube is given by the formula V = s^3, where s is the length of one side of the cube.

Multiple choice

A cube is a three-dimensional geometric figure that has six square faces. What is the volume of a cube with side length 4?

  1. 64

  2. 128

  3. 192

  4. 256
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cube with side length s is given by the formula s^3. Therefore, the volume of a cube with side length 4 is 4^3 = 64.

Multiple choice

A pyramid is a three-dimensional geometric figure that has a polygonal base and triangular sides that meet at a common point (the apex). What is the volume of a pyramid with square base side length 6 and height 8?

  1. 96

  2. 192

  3. 288

  4. 384
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a pyramid with square base side length s and height h is given by the formula (1/3)s^2h. Therefore, the volume of a pyramid with square base side length 6 and height 8 is (1/3) * 6^2 * 8 = 96.

Multiple choice

What is the volume of a cube with side length 4?

  1. 16

  2. 32

  3. 64

  4. 128
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a cube is given by the formula $V = a^3$. Substituting the given value, we get $V = 4^3 = 64$.

Multiple choice

What is the volume of a cube with side length 4 cm?

  1. 64 cm^3

  2. 128 cm^3

  3. 192 cm^3

  4. 256 cm^3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cube is given by the formula s^3. Therefore, the volume of a cube with side length 4 cm is 4^3 = 64 cm^3.

Multiple choice

What is the name of the mathematical problem that involves finding the volume of a sphere?

  1. Volume of a Cube

  2. Volume of a Pyramid

  3. Volume of a Sphere

  4. Volume of a Cone
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a sphere is given by the formula (4/3)πr³, where r is the radius of the sphere.

Multiple choice

Brahmagupta's formula for finding the volume of a pyramid is:

  1. $V = \frac{1}{3}Bh$
  2. $V = \frac{1}{3}Ah$
  3. $V = \frac{1}{3}Bh^2$
  4. $V = \frac{1}{3}Ah^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's formula for finding the volume of a pyramid is $V = \frac{1}{3}Bh$.

Multiple choice

Find the volume of a cube with side length 5 cm.

  1. 125 cm³

  2. 25 cm³

  3. 15 cm³

  4. 5 cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cube is given by V = a³, where a is the length of one side. In this case, a = 5 cm, so V = 5³ = 125 cm³.