Question

A right circular cone is $5.8cm$ high and radius of its base is $3.4cm$. It is melted and recast into a right circular cone with radius of its base $1.7cm$. Find its height.

• A. $20.2cm$
• B. $21.2cm$
• C. $23.2cm$
• D. $22.2cm$

Answer 1

The correct option is C $23.2cm$

Given, height of cone${}_1=$ $h_1=5.8cm$

and the radius of the base $r_1=3.4cm$

Also, the radius of the base of second cone $r_2=3.4cm$

Let the height of the second cone be $h$

Given: Volume of cone${}_1=$ Volume of cone${}_2$

$\Rightarrow$ $\frac{1}{3}\pi r_1^2{h}_1=\frac{1}{3}\pi r_2^2{h}_2$

$\Rightarrow$$\frac{1}{3}\times \pi \times {\left(3.4\right)}^2\times 5.8=\frac{1}{3}\times \pi {\left(1.7\right)}^2\times h$

$\Rightarrow$$h=\frac{{\left(3.4\right)}^2\times 5.8}{{\left(1.7\right)}^2}$

$=23.2cm$