Question

A rectangular block of wood has dimensions $24$ cm by $8$ cm by $7$ cm. It is cut up into children's bricks.
Each brick is a cube of side $3$ cm

Find the volume of wood that is left.

Answer 1

Let 'n' be the no of brick cut

$\Rightarrow$ Vol. of cuboid $=n\times$ vol. of cube

$\Rightarrow 7\times 8\times 24=n\times 3^3$

$\Rightarrow n=49.78$ $\therefore$ no of brick

that can be cut out is $49$

Vol. left $=$ Vol. of cuboid $-\left(49\right)$ Vol. of cube

$=(7\times 8\times 24)-49\left(3^3\right)=21$