Cone

Example 1:

Find the lateral surface area of a right cone if the radius is $4$ cm and the slant height is $5$ cm.

$\begin{array}{l}\text{L}\text{.S}\text{.A}\text{.}=\pi \left(4\right)\left(5\right)\\ =20\pi \\ \approx 62.8{\text{ cm}}^2\end{array}$

Example 2:

Find the total surface area of a right cone if the radius is $6$ inches and the slant height is $10$ inches.

$\begin{array}{l}\text{T}\text{.S}\text{.A}\text{.}=\pi \left(6\right)\left(10\right)+\pi {\left(6\right)}^2\\ =60\pi +36\pi \\ =96\pi {\text{ in}}^2\\ \approx 301.59{\text{ in}}^2\end{array}$

Example 3:

Find the volume of a cone whose altitude is $15$ m and whose radius is $8$ m.

$\begin{array}{l}V=\frac{1}{3}{\left(8\right)}^2\left(\pi \right)\left(15\right)\\ =320\pi \\ \approx 1005.31\end{array}$

Therefore, the volume of the cone is about $1005.31{\text{ m}}^3$ .