SOLUTION: Height of cone is 8cm and curved surface area is 188.4cm sq. Then find the volume of cone.

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Question 550972: Height of cone is 8cm and curved surface area is 188.4cm sq. Then find the volume of cone.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Height of cone is 8cm and curved surface area is 188.4cm sq.
Then find the volume of cone.
:
The curved portion surface area of a cone: A+=+pi%2Ar%2Asqrt%28r%5E2%2Bh%5E2%29
:
Find r
pi%2Ar%2Asqrt%28r%5E2%2B8%5E2%29 = 188.4
r%2Asqrt%28r%5E2%2B64%29 = 188.4%2Fpi
r%2Asqrt%28r%5E2%2B64%29 = 59.9696
Square both sides
r%5E2%28r%5E2%2B64%29 = 3596.35
r%5E4%2B64r%5E2+-+3596.35 = 0
solve this with the quadratic formula
the positive solution
r^2 ~ 36, which is what we want to find the volume
:
Find the volume; V+=+1%2F3*pi%2Ar%5E2%2Ah
V+=+1%2F3*pi%2A36%2A8
V = 301.6 cu cm