Question

Two cones with same base radius $8$ cm and height $15$ cm are joined together along their bases. Find the surface area of the shape so formed (answer to the nearest whole number).

Answer 1

When two cones of same base are joined together, the surface of the shape formed will only have the curved surfaced areas visible.

We know, curved surface area of a cone $=\pi rl$, where $r$ is the radius of the cone and $l$ is the slant height.

As both the cones have the same base and height, they are identical and their curved surface areas are equal.

Hence, surface area of this shape $=$ Curved surface area of Cone 1 $+$ Curved surface area of Cone $2=2\times \left(\pi rl\right)$.

Given, $r$ $=8$ cm and $h$ $=15$ cm.

Then, slant height $l=\sqrt{r^2+h^2}=\sqrt{8^2+{15}^2}=\sqrt{64+225}=17$ cm.

Therefore, surface area of this shape $=2\times \left(\pi rl\right)=2\times \frac{22}{7}\times 8\times 17=854.86c{m}^2\approx 855{cm}^2$.

Hence, the required surface area is $855c{m}^2$.