Question

The total surface area of a metallic hemisphere is $1848c{m}^2$. The hemisphere is melted to form a solid right circular cone. If the radius of the base of the cone is the same as the radius of the hemisphere, its height is

• A. $42cm$
• B. $26cm$
• C. $28cm$
• D. $30cm$

Answer 1

The correct option is C $28cm$

Total surface area of hemisphere $=3\pi r^2$, where $r=$ radius of hemisphere.
$\therefore 3\pi r^2=1848$
$\Rightarrow 3\times \frac{22}{7}\times r^2=1848\Rightarrow r^2=\frac{1848\times 7}{3\times 22}=196$
$r=\sqrt{196}=14cm$
Volume of hemisphere $=\frac{2}{3}\pi r^3$
$=\frac{2}{3}\times \pi \times 14\times 14\times 14c{m}^3=\frac{5488}{3}\pi c{m}^3$
According to the question,
Volume of cone $=$ Volume of hemisphere
$\Rightarrow \frac{1}{3}\pi r^{2}h=\frac{5488}{3}\pi c{m}^3\Rightarrow r^{2}h=5488$
$\Rightarrow 14\times 14\times h=5488$
$\therefore h=\frac{5488}{14\times 14}=28cm$.