# Thread: Height of cone

1. ## Height of cone

pls teach me how to start amd solve part (A). thank you very much

2. Originally Posted by helloying
pls teach me how to start amd solve part (A). thank you very much
$\displaystyle OQ$ is the slant height of the cone.

The formula for the Total Surface Area of a cone is

$\displaystyle \textrm{TSA} = \pi r^2 + \pi r s$

where $\displaystyle r$ is the radius and $\displaystyle s$ is the slant height.

Note that $\displaystyle \pi r^2$ is the area of the circular base, so $\displaystyle \pi r s$ is the curved area.

Since you're told that the curved surface has area $\displaystyle 252 \pi \,\textrm{cm}^2$ and the radius $\displaystyle r = 14\,\textrm{cm}$, we have

$\displaystyle 252 \pi \,\textrm{cm}^2 = 14\pi\,\textrm{cm}\cdot s$

$\displaystyle s = \frac{252\pi\,\textrm{cm}^2}{14\pi\,\textrm{cm}}$

$\displaystyle s = 18\,\textrm{cm}$.

You can find the height $\displaystyle OP$ using the Pythagorean Theorem.