SOLUTION: An ice cream cone is packed full of ice cream and a generous hemisphere (half of sphere) of ice cream is placed on top. If the volume of ice cream inside the cone is the same as t

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Question 587936: An ice cream cone is packed full of ice cream and a generous hemisphere (half of sphere) of ice cream is placed on top. If the volume of ice cream inside the cone is the same as the volume of ice cream outside the cone, find the height of the cone (minus the hemisphere) given that the diameter of the hemisphere is 8cm.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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An ice cream cone is packed full of ice cream and a generous hemisphere (half of sphere) of ice cream is placed on top.
If the volume of ice cream inside the cone is the same as the volume of ice cream outside the cone,
find the height of the cone (minus the hemisphere) given that the diameter of the hemisphere is 8cm.
:
Formula for a the volume of a cone: V = 1%2F3pi%2Ar%5E2%2Ah
For the volume of a hemisphere: V = 1%2F2*4%2F3pi%2Ar%5E3
:
With a diameter of 8, the radius = 4 cm
:
1%2F3pi%2A4%5E2%2Ah = 1%2F2*4%2F3pi%2A4%5E3
:
1%2F3pi%2A16%2Ah = 4%2F6pi%2A64
1%2F3pi%2A16%2Ah = 2%2F3pi%2A64
multiply both sides by 3
pi%2A16%2Ah = 2%2Api%2A64
pi%2A16%2Ah = pi%2A128
divide both sides by pi
16h = 128
h = 128/16
h = 8 cm is the height of the cone