Question

If the cost of painting the whole surface area of a cube at the rate of 13 paise per cm² is ₹343.98, then find the volume of the cube.

Answer 1

Cost of painting the cube = ₹348.98
Rate of painting = 13 paise per cm${}^2$
Surface area of the cube
$=\left(\frac{Costofpainting}{Rateofpainting}\right)$
$=\frac{343.98}{0.13}=2,646{\text{cm}}^2$

Let the length of side of the cube be 'a' cm.
Then, its surface area $=6a^2=2,646$
$\Rightarrow a^2=\frac{2,646}{6}=441$
$\therefore a=21\text{cm}$
Hence, the volume of the cube
$=a^3=(21{)}^3=9,261{\text{cm}}^3$