Question

25. One of the silos pictured below holds corn, and the other holds hay. Chopped corn and hay are blown into the tops of the silos through pipes running up from the ground. a. The silos have a radius of 3 meters and a height of 18 meters. What is the volume, to the nearest cubic meter, of one of these silos? b. If a blower can load 1 cubic meter of hay in 3 minutes, how many hours (to the nearest .1 hour) will it take to fill one of these silos?

Answer 1

a. 509 m³

Explanation:

a. Assume that the silos are cylinders with a circular base. The volume of a silo is given by:

`V = \pi *r^2*h`

If the radius (r) is 3 meters, and the height (h) is 18 meters, the volume is:

`V = \pi *3^2*18\\V=509\ m^3`

Total volume is 509 m³

b. If the flow rate is 1 m³ per 3 minutes, the time required to fill the whole 509 m³ is:

`t=509\ m^3*(3\ min)/(1\ m^3)*(1\ h)/(60\ min)\\t=25.45\ h`

It will take 25.45 or roughly 25.5 h to fill one of these silos.