Question

A metallic spherical shell of internal and external diameters $8cm$ and $12cm$, respectively is melted and recast into the form of a cone of base diameter $8cm$. The height of the cone is

• A. $114cm$
• B. $76cm$
• C. $38cm$
• D. $19cm$

Answer 1

Answer: (C)

$38cm$

Volume of a hollow sphere of outer Radius R and inner radius r $=\frac{4}{3}\pi (R^3-r^3)$

Inner radius of the spherical shell $=\frac{8}{2}=4cm$
Outer radius of the spherical shell $=\frac{12}{2}=6cm$
Volume of a cone $=\frac{1}{3}\pi r^{2}h$ where r is the
radius of the base of the cone and h is the height.
Radius of the cone $=\frac{8}{2}=4cm$
Now, Volume of the hollow sphere $=$ Volume of cone
$=>\frac{4}{3}\pi (6^3-4^3)=\frac{1}{3}\pi 4^{2}h$
$=>4\times (216-64)=16h$
$h=38cm$