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satela [25.4K]
3 years ago
14

If a cone has a surface area of 822.78cm^2 and a diameter of 18cm, find the slant height of the cone

Mathematics
1 answer:
Artist 52 [7]3 years ago
8 0

Answer:

20.11\ cm

Step-by-step explanation:

we know that

The surface area of the cone is equal to

SA=\pi r^{2}+\pi rl

where

r is the radius

l is the slant height

In this problem we have

SA=822.78\ cm^{2}

r=18/2=9\ cm -----> the radius is half the diameter

substitute and solve for l

822.78=\pi (9)^{2}+\pi (9)l

822.78=81\pi +9\pi l

l=(822.78-81\pi)/9\pi

l=(822.78-81(3.14))/9(3.14)=20.11\ cm

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