Question

What is the surface area of a right cone with a height of 4 centimeters

and with 3 centimeters as the radius of its base?

Answer 1

`24\pi \: {cm}^(2)`

Explanation:

Given:

A cone

h (height) = 4 cm

r (radius) = 3 cm

Find: A (surface area) - ?

In order to find the surface area, we have to know the length of the slant height first (use the Pythagorean theorem):

`{l}^(2) = {r}^(2) + {h}^(2)`

`{ l}^(2) = {3}^(2) + {4}^(2) = 9 + 16 = 25`

`l > 0`

`l = √(25) = 5 \: cm`

Now, we can find the surface area:

`a(surface) = \pi {r}^(2) + \pi * r * l`

`a(surface) = \pi * {3}^(2) + \pi * 3 * 5 = 9\pi + 15\pi = 24\pi \: {cm}^(2)`