Question

# A right Circular Cone is $3.6\mathrm{cm}$ high and has base radius $1.6\mathrm{cm}$. It is melted and recast into a right circular cone with radius of its base as $1.2\mathrm{cm}$, find its height.

Open in App
Solution

## Step 1: Given informationThe base radius of first right circular cone $\left({r}_{1}\right)$ is $1.6\mathrm{cm}$.The height of first right circular cone $\left({h}_{1}\right)$ is $3.6\mathrm{cm}$.The base radius of second right circular cone $\left({r}_{2}\right)$ is $1.2\mathrm{cm}$. Step 2: Determine the volume of first and second right circular coneWe know that, the volume of right circular cone is $\frac{1}{3}\mathrm{\pi }{\left(r\right)}^{2}\mathrm{h}$, where $r$ is base radius of right circular cone and $h$ is height of first right circular cone.$\begin{array}{rcl}\mathrm{Volume}\mathrm{of}\mathrm{first}\mathrm{right}\mathrm{circular}\mathrm{cone}\left({\mathrm{V}}_{1}\right)& =& \frac{1}{3}×\mathrm{\pi }×{\left(1.6\right)}^{2}×3.6\\ & =& \frac{1}{3}×\mathrm{\pi }×2.56×3.6\\ & =& \frac{9.216}{3}\mathrm{\pi }{\mathrm{cm}}^{3}\end{array}$ $\begin{array}{rcl}\mathrm{Volume}\mathrm{of}\mathrm{second}\mathrm{right}\mathrm{circular}\mathrm{cone}\left({\mathrm{V}}_{2}\right)& =& \frac{1}{3}×\mathrm{\pi }×{\left(1.2\right)}^{2}×3.6\\ & =& \frac{1}{3}×\mathrm{\pi }×1.44×{h}_{2}\\ & =& \frac{1.44}{3}×\mathrm{\pi }×{h}_{2}{\mathrm{cm}}^{3}\end{array}$ Step 3: Determine the height of second right circular cone after recastingSince, second right circular cone is made from first right circular cone, therefore,$\begin{array}{rcl}\mathrm{Volume}\mathrm{of}\mathrm{Second}\mathrm{Right}\mathrm{Circular}\mathrm{Cone}\left({\mathrm{V}}_{2}\right)& =& \mathrm{Volume}\mathrm{of}\mathrm{First}\mathrm{Right}\mathrm{Circular}\mathrm{Cone}\left({\mathrm{V}}_{1}\right)\\ \frac{1.44}{3}×\mathrm{\pi }×{h}_{2}& =& \frac{9.216}{3}×\mathrm{\pi }\\ {h}_{2}& =& \frac{9.216}{1.44}\\ {\mathrm{h}}_{2}& =& 6.4\mathrm{cm}\end{array}$Hence, the height of new right circular cone after recasting is $6.4\mathrm{cm}$.

Suggest Corrections
0
Related Videos
Shape Conversion of Solids
MATHEMATICS
Watch in App
Explore more