SOLUTION: A frustum of a sphere of radius 13 cm is formed by two parallel planes on opposite sides of the center, each at distance of 5 cm from the center. Determine the volume of the frustu

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Question 1203337: A frustum of a sphere of radius 13 cm is formed by two parallel planes on opposite sides of the center, each at distance of 5 cm from the center. Determine the volume of the frustum (a) by using the prismoidal rule, and (b) by using the formula for the volume of a frustum of a sphere
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
A frustum of a sphere of radius 13 cm is formed by two parallel planes on opposite sides of the center, each at distance of 5 cm from the center. Determine the volume of the frustum (a) by using the prismoidal rule, and (b) by using the formula for the volume of a frustum of a sphere
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Find the volumes of the 2 segments NOT in the frustum:
For each:
where r = 13 and and h = 6.5-5 = 1.5
for each
---> 1600pi
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Subtract that from the volume of the shpere:
---> cc
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h = the distance from the surface of the sphere to the plane on the diameter.
PS This is an equation used in the calculation of the volume of a liquid in a spherical tank where h would be the depth of the liquid.
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I mistakenly used 13 as the diameter when it's the radius.
The method is good, tho.
The student can redo it using 13 instead of 6.5

Answer by ikleyn(52810)   (Show Source):
You can put this solution on YOUR website!
.

Alan, what is

        h = 6.5-5 = 1.5

in your solution ?

I want to ask, what " 6.5 " does represent there ?

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Alan, don't you think that h should be   h = 13-5 = 8 cm ?