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 maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

Each piece of cardboard is $0.3\ cm$ thick. If Marie stacks $8$ pieces of cardboard on top of one another, how thick will the stack be?

  1. $2.4\ cm$
  2. $24\ cm$
  3. $2.1\ cm$
  4. $21\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

It is given that each piece of cardboard is $0.3$ cm thick which means that one piece is $0.3$ cm thick.


If Marie stacks $8$ pieces of cardboard, then the thickness of $8$ pieces of cardboard will be:

$0.3\times 8=2.4$ cm

Hence, the stack will be $2.4$ cm thick.

Multiple choice maths the trapezium rule approximation errors and approximations the need for approximation

Find the approximate error in the volume of a cube with edge $x$ cm, when the edge is increased by $2\%$

  1. $4\%$
  2. $2\%$
  3. $6\%$
  4. $8\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

in a mutiplication while multiplying we have to add the percentage errors 


so if the edge of the cube is $x$cm then the volume will be ${ x }^{ 3 }$

but for errors we have to add the percentage 

therefore the total error  percentage now becomes $6\%$

therefore the error is increased by $4\%$

Multiple choice maths the trapezium rule approximation errors and approximations the need for approximation

If there is an error of $k%$ in measuring the edge of a cube, then the percent error in estimating its volume is

  1. $k$
  2. $3k$
  3. $\displaystyle \frac{k}{3}$

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

Volume of cube$V=x^{3}$
$\displaystyle \frac{dV}{dx}=3x^{2}$
Percentage error in measuring side $= k%$
$\displaystyle \Rightarrow \frac{\delta x}{x}=\frac{k}{100}$
$\displaystyle {\delta{x}}=\frac{xk}{100}$
Approximate error in estimating volume $=dV=(\frac{dV}{dx}){\delta x}=3x^{2}\frac{xk}{100}$
Percentage error in estimating volume$=\frac{dV}{V}\times 100=3k$

Multiple choice maths the trapezium rule approximation errors and approximations the need for approximation

The percentage error in the surface area of a cube with edge x cm, when the edge is increased by $11\%$ is _________.

  1. $11$
  2. $22$
  3. $10$
  4. $44$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Surface area of cube $=$ S $=6x^2$
$\therefore \dfrac{dS}{dt}=12x\dfrac{dx}{dt}$
Side of cube increase $11\%$.
$\therefore \dfrac{dx}{dt}=11\%$ increment in side
$=\dfrac{11x}{100}$
$\therefore \dfrac{dx}{dt}=12\left(\dfrac{11x}{100}\right)$
$=6\left(\dfrac{22}{100}\right)x^2$
$=6x^2\left(\dfrac{22}{100}\right)$
$=22\%$ in surface area
$\therefore$ Surface area increase $22\%$.

Multiple choice chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

The density of a cuboid of mass 200 g with dimensions 2 cm $\times$ 4 cm $\times$ 5 cm is

  1. 1000 kg m$^{-3}$
  2. 3000 kg m$^{-3}$
  3. 5000 kg m$^{-3}$
  4. 2000 kg m$^{-3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The density of a body is defined as the amount of substance contained per unit volume.
Density $=\dfrac{mass}{volume}$

$\displaystyle d = \frac{0.2 kg}{40  cm^3} = \frac{0.2 \times 10^6}{40} kg  m^{-3}$

$=5000  kg  m^{-3}$
Multiple choice

If you have a cube, how would you calculate its volume?

  1. by dropping into a graduated with water

  2. by water displacement

  3. by measuring its sides with a ruler

  4. by using a triple beam balance
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a regular cube, measuring side length with a ruler and calculating volume as side cubed is the most direct method. Water displacement can measure volume indirectly but is less precise for geometric shapes, while a triple beam balance measures mass.

Multiple choice

A side of a cube which volume is 27m3 is

  1. 30m

  2. 9m

  3. 300cm

  4. 0.9m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a cube is s^3 = 27. Thus, s = cbrt(27) = 3 meters. Converting 3 meters to centimeters gives 3 * 100 = 300 cm.

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

The maximum error in the measurement of mass and density of a cube are 3% and 1% respectively. The maximum error in the measurement of volume will be:

  1. 1%

  2. 2%

  3. 3%

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

$\displaystyle V=\frac {m}{d}$

$\displaystyle \frac {\Delta V}{V}\times 100=(\frac {\Delta m}{m}+\frac {\Delta d}{d})\times 100=(3+1)=4$%

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 can be measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are 3% and 2% respectively, the maximum error in the measurement of the density of the cube is :

  1. 9%

  2. 19%

  3. 10%

  4. 90%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$ d = ML^{-3}\rightarrow  (By \   dimensional \  analysis)$


$\displaystyle \frac{\triangle d}{d} = \frac{\triangle M}{M}+ 3\frac{\triangle L}{L}$
          $ = 3+3(2)$
          $ = 9$%