# How to Calculate the Surface Area of cone with radius of 1.8cm and height of 2.4cm?

Mar 1, 2018

$27.1296 c {m}^{2}$

#### Explanation:

The formula for the surface area of a cone is $S a = \pi r l + \pi {r}^{2}$
$S a$ = surface area
$r$ = radius
$l$ = slant height
From the given information, we already have some of the numbers. We know that
$r$ = 1.8 cm
$\pi$ = 3.14
$h$ = 2.4 cm
However, we do not know the slant height of the triangle. Using this picture below as a guide, you can fill in $r$ and $h$

Using the Pythagorean Theorem (${a}^{2} + {b}^{2} = {c}^{2}$), we can find $l$

We can say that ${h}^{2} + {r}^{2} = {l}^{2}$ by using substitution. So lets plug the numbers into this equation.
${2.4}^{2} + {1.8}^{2} = {l}^{2}$
$5.76 + 3.24 = {l}^{2}$
$9 = {l}^{2}$
$\sqrt{9} = l$
$3 = l$

Yay! We've solved the first part. Now that we know all our variables, we can plug that into the first equation.
$S a = \pi r l + \pi {r}^{2}$
$S a = 3.14 \left(1.8\right) \left(3\right) + 3.14 \left({1.8}^{2}\right)$
$S a = 16.956 + 10.1736$
$S a = 27.1296 c {m}^{2}$