SOLUTION: find the surface area and volume of a cone with a slant hieght of 17 and a base with circumference 16∏

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Question 753636: find the surface area and volume of a cone with a slant hieght of 17 and a base with circumference 16∏
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
If the base has a circumference of 16 pi
and circumference = pi * diameter
then the base has a radius of 8 (diameter/2)
Surface Area of Cone = pi*r^2 + pi*r*s (s - slant height)
= pi* 8^2 + pi* 8 * 17
= 628.3 (1 decimal place)
Volume of Cone = 1/3 pi * r^2 * h
To find h we must construct a right angled triangle
The hypotenuse is the slant height and the radius
is the base. h is the other side.
So h^2 + 8^2 = 17^2
h^2 = 17^2 - 8^2
h = square root of 17^2 - 8^2
h = 15
So Volume of Cone = 1/3 * pi * 8^2 * 15
= 1005.3 (1 decimal place)
Hope this helps
:-)