Question

A right circular cone is of height $3.6$ cm and radius of its base is $1.6$ cm . It is melted and recasted into a right circular cone with radius of its base $1.2$ cm. Find the height of the cone so formed.

• A. $6.4$ cm
• B. $6$ cm
• C. $4.8$ cm
• D. $4$ cm

Answer 1

Answer: (A)

As the cone is melted and recasted in to another cone, Volume of both the cones are equal.
Volume of a cone $V=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius of the base of the cone and $h$ is the height.
Let $h$ be the height of the new cone formed.

Given, in original cone, height $h=3.6cm$ and radius $r=1.6cm$.

Also, in new cone, radius $r=1.2cm$.
Now, $V_1=V_2$
Thus $\frac{1}{3}\pi \times {1.6}^2\times 3.6=\frac{1}{3}\pi \times {1.2}^2\times h$
$\Rightarrow h=6.4$ cm.

Hence, option $A$ is correct.