Question

Find the total surface area of a right circular cone with a radius of $6cm$ and height $8cm$.

Answer 1

Step 1: Find the slant height of the cone.

Let the slant height of the cone $lcm$

Given that, the radius $r$ of the cone is $6cm$ and the height $h$ of the cone is $8cm$

According to the Pythagoras theorem, $l^2=h^2+r^2$

$$\begin{gathered} \Rightarrow l^2=8^2+6^2 \\ \Rightarrow l^2=64+36 \\ \Rightarrow l^2=100 \\ \Rightarrow l=10cm \end{gathered}$$

Step 2: Find the total surface area of the cone

The total surface area of the cone of radius $r$ and slant height $l$ $=\mathrm{\pi r}\left(\mathrm{r}+\mathrm{l}\right)$

$$\begin{gathered} =\frac{22}{7}\times 6\left(6+10\right) \\ =\frac{22}{7}\times 6\times 16\left(\pi =\frac{22}{7}\right) \\ =301.71c{m}^2 \end{gathered}$$

Hence, total surface area is $301.71c{m}^2$