Question

How many spherical lead shots, each of radius $1\mathrm{cm}$ can be made from a sphere of radius $4\mathrm{cm}$ ?

• A. $32$
• B. $16$
• C. $64$
• D. $48$

Answer 1

The correct option is C

$64$

Step 1: Given data

Radius of bigger sphere, $R=4cm$

Radius of spherical lead shot, $r=1cm$

Number of smaller spheres that can be made from bigger sphere, $n=?$

Step 2: Calculating the number of spherical lead shots

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

Volume of bigger sphere$=n\times$spherical lead shots

$$\begin{gathered} \frac{4}{3}{\mathrm{\pi R}}^3=n\times \frac{4}{3}{\mathrm{\pi r}}^3 \\ {\mathrm{R}}^3=\mathrm{n}\times {\mathrm{r}}^3 \\ \mathrm{n}=\frac{{\mathrm{R}}^3}{{\mathrm{r}}^3}=\frac{4\times 4\times 4}{1\times 1\times 1}=64\mathrm{spheri}c\mathrm{al}\mathrm{lead}\mathrm{shots} \end{gathered}$$

Therefore, $64$ spherical lead shots is needed.

Hence, option C is correct.