A grain silo is constructed in the shape of a cylinder with hemispherical roof.?The hemisphere and the cylinder have the same radius. The height of the cylinder equals the radius of the cylinder. What is the ratio of the volume of the grain silo to its surface area (as an algebraic expression of the radius) As the radius. volume of cylinder=___________(in terms of pi) Volume of hemisphere =_________(in terms of pi) Total volume of grain silo=_________(in terms of pi) Surface area of the grain silo=__________(in terms of pi) Ratio of Volume to Surface area =___________(this is not a number it's an algebraic expression)
All silos are not tall cylinders. Some are piles above the ground and some are trench's in the ground. Upright silos, such as you are talking about are losing favor because they hold relatively little feed and with today's larger operations it takes a lot of them to store feed. Recently silage has been forced into large plastic bags laying on the ground. These provide good storage also.
vol of cyl = pi x r^2 x r = pi r^3 vol of hemisphere = 1/2 x 4/3 pi r^3 = 2/3 pi r^3 total vol = 5/3 pi r^3 surface = 1/2 x 4 pi r^2 for hemisphere pi r^2 for floor and 2pir^2 for wall surface = 5 pi r^2 vol/surf = r/3
