Question

A piece of metal in the form of a cone of radius $\mathbf{3}\mathbf{}\mathbf{cm}$ and height $\mathbf{7}\mathbf{}\mathbf{cm}$ is melted and cast into a cube. Find the side of the cube.

Answer 1

Step 1: Given information.

The radius of the cone $\left(r\right)=3\mathrm{cm}$

The height of the cone $\left(h\right)=7\mathrm{cm}$

Step 2: Calculate the side of the cube.

Let the side of the cube be $a\mathrm{cm}.$

Since the piece of metal in the form of a cone is melted and cast into a cube, the volume of the cone and the volume of the cube will be equal.

$$\begin{gathered} \therefore \mathrm{Volume}\mathrm{of}\mathrm{cube}=\mathrm{Volume}\mathrm{of}\mathrm{cone} \\ \Rightarrow a^3=\frac{1}{3}\mathrm{\pi }{r}^{2}h \\ \Rightarrow a^3=\frac{1}{3}\times \frac{22}{7}\times 3^2\times 7 \\ \Rightarrow a^3=22\times 3=66 \\ \Rightarrow a=\sqrt[3]{66} \\ \Rightarrow a=4.04\mathrm{cm} \end{gathered}$$

Hence, the side of the cube is $4.04\mathrm{cm}.$