Question

Rachana makes a cuboid of plasticine of sides $5cm,2cm$ and $5cm$.

How many such cuboids will she need to form a cube?

Answer 1

Let length of cuboid is $\mathrm{l}$, breadth of cuboid is $\mathrm{b}$ and height of cuboid is $\mathrm{h}$

Let

$\mathrm{l}=5\mathrm{cm}$, $\mathrm{b}=2\mathrm{cm},\mathrm{h}=5\mathrm{cm}$

We know that

Volume of cuboid $=\mathrm{lbh}$

$\Rightarrow$Volume of cuboid $=5\times 2\times 5c{m}^3=50c{m}^3$

Now

LCM of $5,2,5=10$

$\Rightarrow$The least length of cube $\left(a\right)$ $=10cm$

Volume of cube $=a^3$

$={10}^3$

$=1000c{m}^3$

Number of cuboids required to make the bigger cube $=$ $\frac{\mathrm{Volume}\mathrm{of}\mathrm{cube}}{\mathrm{Volume}\mathrm{of}\mathrm{cuboid}}$

$=\frac{1000}{50}$

$=20$

Hence $20$ such cuboids are required to make a cube