Problema Solution
A grain silo consists of a cylindrical main section and a hemispherical roof. The cylindrical part is 30 ft tall. Express the total volume of the silo (including the part inside the roof section) as a function of the radius of the silo.
Answer provided by our tutors
The total volume of the silo is a sum of
V1 = the volume of the cylinder with radius 'r' and height 30 ft and
V2 = the volume of a half sphere with radius r that makes the hemispherical roof
Volume of the cylinder V1 = (r^2) * pi * h where h = 30 ft, that is V1 = 30 pi * (r^2)
Volume of half sphere with radius r is V2 = 0.5 * (4/3) * pi * (r^3)
The total volume of the silo is
V = V1 + V2
V = 30 pi * (r^2) + 0.5 * (4/3) * pi * (r^3)
V = 30 pi * (r^2) + (2/3) * pi * (r^3) - is a function of the radius of the silo r.