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 largest number of bricks that can be cut from the block.

Answer 1

Given: Length of rectangular block $\left(l\right)=24cm$

Breadth of rectangular block $\left(b\right)=8cm$

Height of rectangular block $\left(h\right)=7cm$

Side of cubical brick $\left(s\right)=3cm$

Let the number of bricks that can be cut from the block be given by

Volume of rectangular block $=n\times$ Volume of cubical brick

$\Rightarrow lbh=n\times s^3$

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

$\Rightarrow 24\times 8\times 7=n\times 27$

$\Rightarrow n=\frac{24\times 8\times 7}{27}$

$\Rightarrow n=49.77$

So, Largest number of bricks that can b be cut from the block $=49$.