SOLUTION: A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). The diameter of the silo is to be 30 feet, but t

Question 988651: A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). The diameter of the silo is to be 30 feet, but the height is yet to be determined. Find the height h of the silo that will result in a capacity of 13,500π ft3.
I got 50 as the height by 13500π= (1/2(4/3*15^3))+((15^2)h) and solving for h. however i was told the answer is 65

Found 2 solutions by Boreal, solver91311:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The height is the height of the cylinder plus the radius of the hemisphere on top.
Volume of the height part is V=pi*r^2h=225pi*h
The hemisphere has volume (2/3)*pi*15^3, since the "height" of the top is really the radius of the hemisphere. That is 2250pi
That leaves 225pi*h=11,250 pi, subtracting the top.
11250 pi/225 pi=50, as you had.
BUT, that is the height of the non-hemisphere part.
The hemisphere itself is the radius high, or 15 feet in its own right.
So the sum of 50+15 is 65 feet.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Your arithmetic is correct, but remember that is the height of the cylindrical portion of the silo. The hemispherical portion, having a radius of 15 feet, extends 15 feet higher than the top of the cylinder part. 50 plus 15 is 65.

John

My calculator said it, I believe it, that settles it

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