Question

Ravi made a cuboid of plasticine of dimensions$12cm,8cm$ and $3cm.$ How many minimum numbers of such cuboids will be needed to form a cube of side $12cm$?

Answer 1

Step 1: Find volume of cube

The given side of cube $=12cm$ and

Cuboid dimensions are $\mathrm{length}\left(\mathrm{l}\right)=12\mathrm{cm},\mathrm{breadth}\left(\mathrm{b}\right)=8\mathrm{cm},\mathrm{height}\left(\mathrm{h}\right)=3\mathrm{cm}.$

$\Rightarrow$ Volume of cube $={\left(side\right)}^3$

$$\begin{gathered} ={\left(12\right)}^3 \\ =1728c{m}^3 \end{gathered}$$

Step 2: Find number of cuboids.

Now, Volume of cuboid $=\mathrm{lbh}$

$$\begin{gathered} =12\times 8\times 3 \\ =288{\mathrm{cm}}^3 \end{gathered}$$

Number of cuboids needed to form such cubes$=\frac{\mathrm{volume}\mathrm{of}\mathrm{cube}}{\mathrm{volume}\mathrm{of}\mathrm{a}\mathrm{cuboid}}$

$$\begin{gathered} =\frac{1728}{288} \\ =6 \end{gathered}$$

Hence $6$ such cuboids will be needed to form a cube of side $12cm.$