SOLUTION: A plane is passed through a right circular cone parallel to the base and 0.6 m from the vertex. The altitude and basal diameter of the cone are 1.5 m and 1.2 m, respectively. Find

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Question 1198560: A plane is passed through a right circular cone parallel to the base and 0.6 m from the vertex. The altitude and basal diameter of the cone are 1.5 m and 1.2 m, respectively. Find the volume of the frustum of this cone.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The volume of the original cone in cubic meters is

V=%281%2F3%29%28pi%29%28r%5E2%29%28h%29=%281%2F3%29%28pi%29%280.6%5E2%29%281.5%29=0.18

The small cone cut off from the original cone has a height of 0.6m, which is 2/5 the height of the original cone. That makes the volume of that small cone (2/5)^3 = 8/125 of the volume of the original cone.

So then the volume of the frustum is 117/125 of the volume of the original cone.

ANSWER: Volume of frustum = (0.18)(117/125) = 0.16848 cubic meters

You can also find the volume using the formula for the volume of a frustum:

V=%281%2F3%29%28R%5E2%2BRr%2Br%5E2%29%28h%29

Where R and r are the radii of the two bases and h is the height of the frustum:

V=%281%2F3%29%28%280.6%5E2%29%2B%280.6%2A0.24%29%2B%280.24%5E2%29%29%280.9%29+=+0.16848