Question

A right circular cone is $3.6cm$ high and radius of its base is $1.6cm$. It is melted and recast into a right circular cone with radius of its base as $1.2cm$. Find its height.

• A. $6.4cm$
• B. $5.4cm$
• C. $6.8cm$
• D. $4.4cm$

Answer 1

The correct option is A $6.4cm$

Radius of first cone, $r_1=1.6cm$
and height of first cone, $h_1=3.6cm$.

Radius of second cone, $r_2=1.2cm$
and height of second cone, $=h_{2}cm$.
Now, volume of the first cone$=$volume of second cone
$⟹$ $\frac{1}{3}\pi {r_1}^2{h}_1=\frac{1}{3}\pi {r_2}^2{h}_2$

$⟹$${\left(1.6\right)}^2\times 3.6={\left(1.2\right)}^2\times h_2$

$⟹$$h_2=6.4cm$.

Hence, option $A$ is correct.