Question

Question 1
A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.

Answer 1

Let height of the cone be $h_1$
Given, radius of the base of the cone = 6 cm
$\therefore$ Volume of circular cone
$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi (6{)}^{2}h=\frac{36\pi h}{3}=12\pi hc{m}^3$

Also. Given radius of the hemisphere = 8 cm
$\therefore Volumeofthehemisphere=\frac{2}{3}\pi r^3=\frac{2}{3}\pi (8{)}^3=\frac{512\times 2\pi }{3}$

$\because Volumeofthehemisphere=Volumeofthecone$

$\therefore \frac{512\times 2\pi }{3}=12\pi h\Rightarrow h=\frac{512\times 2\pi }{12\times 3\pi }=\frac{256}{9}=28.44cm$

$\therefore Heightofthecone,h=28.44cm$