Question

A cube & cuboid have the same volume the dimensions of the cuboid are in the ratio $1:2:4$ . If the difference between the cost of painting and cube (whole surface area) at the rate of $Rs.5persq.mts$ is $Rs.80$. Find their volume.

Answer 1

Let volume of cube$=V$

Volume of cuboid$=V=8L^3$

$\therefore$Side of cube$=2L$

Now, $6{\left[2L\right]}^2\times 5-2[2L^2+8L^2+4L^2]\times 5=\pm 80$

$\Rightarrow 120L^2-140L^2=-80$

$\Rightarrow 20L^2=80$

$\Rightarrow L^2=4\Rightarrow R=2$

$\therefore$Volume$=8\times L^3$

$=64m^3$