SOLUTION: A plane slices a right circular cone parallel to its base at the midpoint of its height. The radius of the cone is 4 in. and its height is 12 in. Find the volume of the figure BELO

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Question 1192229: A plane slices a right circular cone parallel to its base at the midpoint of its height. The radius of the cone is 4 in. and its height is 12 in. Find the volume of the figure BELOW the plane. ​
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
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frustum


the bottom portion of the cone is called a frustum
use the formula: volume V=+%281%2F3%29+%2Api%2A+h%5B1%5D+%2A+%28r%5E2%2B+r+%2A+r%5B1%5D+%2B+r%5B1%5D%5E2%29 , where r is a radius of the base of a cone, and r%5B1%5D of top surface of a frustum radius.
given:
r is a radius of the base r=4in, height h=12in
and if the midpoint of its height top of the frustum-> h%5B1%5D=6in and radius must be r%5B1%5D=2in

then,
V+=+%281%2F3%29%2Api%2Ah1%2A%28r%5B1%5D%5E2%2Br%5E2%2B%28r%5B1%5D%2Ar%29%29

V+=+175.93in%5E3

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
A plane slices a right circular cone parallel to its base at the midpoint of its height.
The radius of the cone is 4 in. and its height is 12 in. Find the volume of the figure BELOW the plane.
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The volume of the large cone is  %281%2F3%29%2Api%2Ar%5E2%2Ah = %281%2F3%29%2Api%2A4%5E2%2A12 = 64%2Api  in^3.



The volume of the small (cut) cone is  1%2F8  of the volume ​of the large cone.


So, the cut volume is  8pi  in^3,  and the bottom part volume is  64pi - 8pi = 56pi in^3.    ANSWER

Solved.