Question

The cost of painting the whole surface area of a cube at the rate of $Rs.10\,\,per\,c{m^2}$ is $Rs.264.40\,c{m^2}$, then the volume of the cube is

A) $6.859c{m^3}$
B) $9.261c{m^3}$
C) $8.000c{m^3}$
D) $10.648c{m^3}$

Answer 1

Hint: We have given the total cost for painting and the rate of painting so from these two values we will find the total surface area of the cube further giving us the side measurement of the cube. Now using the formula of the volume of a cube we will find the volume of the cube.

Complete step by step solution: Given data: Rate of painting the surface of the cube $ = Rs.10/c{m^2}$

Total cost for painting $ = Rs.264.40$

We know that the total surface area of a cube $ = 6{(side)^2}$

We know that,

the total cost of painting the whole surface of the cube $ = $ total surface area of the cube $ \times $ rate of painting

Therefore, the total surface area of the cube $ = $ total cost of painting the / rate of painting

The total surface area of the cube $ = \dfrac{{264.40}}{{10}}$

$ \Rightarrow 6{(side)^2} = 26.44$

Dividing both sides by 6

$ \Rightarrow {(side)^2} = 4.406$

Taking square root on both the sides

$ \Rightarrow side = 2.099$

The volume of a cube $ = {(side)^3}$

\[ = {\left( {2.099} \right)^3}\]

On cubing we get,

$ = 9.247c{m^3}$

Hence, the volume of the cube is $9.247c{m^3}$.

Option(B) is correct, as taken in approximation.

Note: While taking the surface area of the cube most of the students take it as the curved surface area of the cube which is not correct as it is given in the question that the cost of the painting of the whole area which means the total surface area, so remember not to take the area as the curved surface area.