SOLUTION: A hemisphere of the radius 3 inches sits on top pf a cylinder of radius 3 inches. The entire solid is 12 inches tall. What is its volume of the entire solid?

Click here to see ALL problems on Volume

Question 104128: A hemisphere of the radius 3 inches sits on top pf a cylinder of radius 3 inches. The entire solid is 12 inches tall. What is its volume of the entire solid?
Answer by TP(29) (Show Source):
You can put this solution on YOUR website!
Since the hemisphere has height(radius) 3 inches then the height of the cylinder must be 9 inches(since you are told that the total height is 12 inches).
Now the formula for the volume of a cylinder is pi*(radius)^2*(height) and so the cylinder has volume 3.142*3^2*9=254.469 cubic inches.
Now the formula for the volume of a sphere is (4*pi*(radius)^3)/3.
This means that the formula for a hemisphere is a half of this.
And so the volume of a hemisphere is (2*pi*(radius)^3)/3.
So our hemisphere must have a volume of (2*3.142*(3)^3)/3 = (6.284*27)/3 = 56.556 cubic inches.
The total volume then is 254.469+56.556 cubic inches =311.025 cu.ins.ANS