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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?

User Jagz S
by
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1 Answer

1 vote

Answer:


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)

User Mick Mnemonic
by
7.4k points

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