Question

Parikshit makes a cuboid of plasticine of sides $\mathit{5}\mathrm{cm},\mathit{2}\mathrm{cm}\mathrm{and}\mathit{5}\mathrm{cm}$. How many such cuboids will he need to form a cube?

Answer 1

Find a number of cuboids required to form a cube.

Given, that the dimensions of a cuboid are $5\mathrm{cm},2\mathrm{cm},5\mathrm{cm}$

The volume of the cuboid $=\mathrm{length}\times \mathrm{breadth}\times \mathrm{height}$

$$\begin{gathered} \therefore \mathrm{Volume}=5\times 2\times 5 \\ =5^2\times 2{\mathrm{cm}}^3 \end{gathered}$$

As there are two $5\text{'}s$ and one $2$, to make the volume of a cuboid as a cube number we need to multiply it by $5\times 2\times 2$

Newly formed cube $=5^2\times 2^1\times 5\times 2\times 2=5^3\times 2^3{\mathrm{cm}}^3$

Number of cuboids required $\mathbf{=}\frac{\mathbf{Volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{cube}}{\mathbf{Volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{cuboid}}$

Number of cuboids required $=\frac{5^3\times 2^3}{5^2\times 2}=5\times 2\times 2=20$

Hence, $20$ cuboids are needed to make a perfect cube.