Question

A solid piece of iron in the form of a cuboid of dimensions $49cm\times 33cm\times 24cm$ is moulded to form a solid sphere.

The radius of the sphere is

• A. $21cm$
• B. $23cm$
• C. $25cm$
• D. $19cm$

Answer 1

The correct option is A

$21cm$

For given cuboid$,$

Length $\left(l\right)=49cm$

Breadth $\left(b\right)=33cm$

Height $\left(h\right)=24cm$

The cone is moulded to form a solid sphere

We have to determine the radius of the sphere

According to the given parameters

Volume of cuboid$=lbh$

The volume of given cuboid $=49\times 33\times 24c{m}^3$

The cube is moulded to sphere

Let the radius of sphere be $r.$

As volume of sphere $=\frac{4}{3}{\mathrm{\pi r}}^3$

Volume of cuboid $=$ volume of sphere molded

$$\begin{gathered} \Rightarrow 49\times 33\times 24=\frac{4}{3}{\mathrm{\pi r}}^3 \\ \Rightarrow {\mathrm{\pi r}}^3=29106 \\ \Rightarrow {\mathrm{r}}^3=29106\times \frac{22}{7} \\ \Rightarrow {\mathrm{r}}^3=9261 \\ \Rightarrow \mathrm{r}=\sqrt[3]{9261} \\ \Rightarrow \mathrm{r}=21\mathrm{cm} \end{gathered}$$