SOLUTION: The diameter of a cone is x cm, the height is 18 cm, and the volume is 96 pi cm cubed. What is x?

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Question 944619: The diameter of a cone is x cm, the height is 18 cm, and the volume is 96 pi cm cubed. What is x?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
For a cone
V=pi%2A+r%5E2+%2A%28h%2F3%29
V=pi%2Ar%5E2%2818cm%2F3%29
V=%28r%5E2%29%286+cm%2Api%29 Divide each side by 6+cm%2Api
V%2F%286+cm%2Api%29=r%5E2
%2896+cu+cm+%2A+pi%29%2F%286+cm+%2A+pi%29=r%5E2
16+sq+cm=r%5E2 find square root of each side
4 cm = r
If x is the diameter, x=2r=8 cm ANSWER diameter is 8 cm
Check
V=96%2Api, h=18 cm, r=4 cm
V=pi%2Ar%5E2%28h%2F3%29
%2896cucm%2Api%29=pi+%2A+4+cm%5E2%2818cm%2F3%29
+96cucm%2Api=pi+%2A+16sqcm%286cm%29
+96cucm%2Api=96cucm%2Api