Question

The largest sphere is carved out of a cube of side $\mathbf{7}\mathbf{}\mathbf{cm}$. Find the volume of the sphere.

Answer 1

Calculate the volume of the sphere:

When the largest sphere is carved out from a cube made of side $7\mathrm{cm}$, the largest sphere will have a diameter of $7\mathrm{cm}$.

The radius of the sphere $\left(r\right)=\frac{7}{2}=3.5\mathrm{cm}$

$\therefore$ The volume of the sphere $\left(V\right)$ is computed as:

$$\begin{gathered} \Rightarrow V=\frac{4}{3}\mathrm{\pi }{r}^3 \\ \Rightarrow V=\frac{4}{3}\times \frac{22}{7}\times {\left(3.5\right)}^3\left[\mathrm{\pi }=\frac{22}{7}\right] \\ \Rightarrow V=\frac{4}{3}\times \frac{22}{7}\times 42.875 \\ \Rightarrow V=179.66{\mathrm{cm}}^3 \end{gathered}$$

Hence, the volume of the sphere is $179.66{\mathrm{cm}}^3$.