Question

The internal and external radii of a metallic spherical shell are $4$ cm and $8$ cm, respectively. It is melted and recast into a solid right circular cylinder of height $9\frac{1}{3}$ cm. Find the diameter of the base of the cylinder.

• A. $16$ cm
• B. $18$ cm
• C. $12$ cm
• D. $14$ cm

Answer 1

Answer: (A)

$16$ cm

Since the spherical shell is recasted into a cylinder,

Volume of the hollow sphere $=$ Volume of the cylinder
Volume of a hollow sphere of outer Radius $R$ and inner radius $r=\frac{4}{3}\pi (R^3-r^3)$
Volume of a Cylinder of Radius "$R$" and height "$h$" $=\pi R^{2}h$
Hence, $\frac{4}{3}\times \pi \times (8^3-4^3)=\pi \times R^2\times \frac{28}{3}$
$\Rightarrow 4\times (512-64)=R^2\times 28$
$\Rightarrow R^2=\frac{4\times 448}{28}=64$ cm
$\Rightarrow R=8$ cm
Hence, diameter of the base of the cylinder $=2\times 8=16$ cm