SOLUTION: A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 78 feet and the radius of the hemisphere is r feet, express the volume of the

Question 348648: A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 78 feet and the radius of the hemisphere is r feet, express the volume of the silo as a function of r.
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
The silo is composed of a cylinder and a hemisphere.
The total volume of the silo = vol. of cylinder + vol. of hemisphere
The volume of a cylinder is given by pi*r^(2)*H where r is the radius of the cylinder and H is the height of the cylinder.
For the silo's cylinder r = r and H = 78 - r. Hence its volume = pi r^(2)*(78 - r)
The volume of a sphere of radius r is (4/3)pi*r^(3). Hence the volume of a hemisphere is (2/3)pi*r^(3).
Hence the volume of the silo = pi r^(2) (78 - r) + (2/3)pi*r^(3)
= pi*r^(2) [ 78 - r/3]

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