Question

Two cones with same base radius $8cm$and height $15cm$ are joined together along their bases. Find the surface area of the shape so formed.

Answer 1

Finding the surface area of the shape so formed.:

Given:

Two cones of same dimensions

Radius $\mathrm{r}=8\mathrm{cm}$

Height $h=15cm$

Total surface area of shape formed$=$Curved area of first cone $+$Curved surface area of second cone

As the cones are identical;

Total surface area of shape formed $=2$( Curved Surface area of cone)

Curved surface area of cone$=\pi rl,$

where

$\begin{array}{rcl}\mathrm{r}& =& \mathrm{radius}\\ \mathrm{l}& =& \mathrm{slant}\mathrm{height}\end{array}$

The total Surface area of shape so formed $=2\pi rl$

$\begin{array}{rcl}& =& 2\times \mathrm{\pi rl}\\ & =& 2\times \mathrm{\pi }\times \mathrm{r}\times \sqrt{({\mathrm{r}}^2+{\mathrm{h}}^2)}\\ & =& 2\times \frac{22}{7}\times 8\times \sqrt{(8^2+{15}^2)}\\ & =& 50.28\times \sqrt{289}\\ & =& 854.85{\mathrm{cm}}^2\\ & =& 855{\mathrm{cm}}^2\left(\mathrm{approx}\right)\end{array}$

Hence, the surface area of shape so formed is $855c{m}^2.$