SOLUTION: Find the total surface area of a cone of base radius 8cm and vertical angle 60

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Question 969942: Find the total surface area of a cone of base radius 8cm and vertical angle 60
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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The vertical angle is 60 degrees so a 30-60-90 triangle is formed with the height as the shorter leg, the radius as the longer leg, and the slant height as the hypotenuse.
To find the surface area we need the slant height (hypotenuse)
For a 30-60-90 right triangle:(radius=longer leg,hypotenuse=slant height)
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Hypotenuse=%28%282%29%28longerleg%29%29%2Fsqrt%283%29
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Slantheight=%28%282%29%288cm%29%29%2Fsqrt%283%29
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Slantheight=%2816cm%29%2Fsqrt%283%29
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Slantheight=9.24cm
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The total surface area of a cone is area of base + lateral surface area:
A=surface area; r=radius=8cm; s=slant height=9.24cm
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A=%28pi%29r%5E2%2B%28pi%29rs
A=%28pi%29%288cm%29%5E2%2B%28pi%29%288cm%29%289.24cm%29
A=pi%2864cm%5E2%29%2Bpi%2873.9cm%5E2%29
A=pi%2864cm%5E2%2B73.9cm%5E2%29
A=137.9%28pi%29cm%5E2