Question

a cylindrical silo has a hemispherical top. the cylinder has a height of 40 m and a base diameter of 12m.

b. the silo should be filled no more than 80% capacity. how much grain can be put in the silo>

c. a truck with a bin measuring 8 m by 4 m by 3.5m delivers grain. how many truckloads would fill a silo to its recommended capacity

Answer 1

Consider the cylindrical silo with hemispherical top as shown in the figure below:

The total volume of the silo is,

$V=\pi (6^2)(40)+\frac{2}{3} \pi (6^3)$

$=1440\pi+144\pi$

$=1584\pi$

The amount of grain put into the silo is,

$A=1584\pi(\frac{80}{100})$

$=1267.20\pi$

The number of truckloads to fill to silo to its recommended capacity of 80% is,

$n=\frac{1267.20\pi}{(8)(4)(3.5)}$

$=\frac{396}{35}\pi$

$\approx 36$

Therefore, the number of truckloads to fill the silo to its recommended capacity is $n\approx36$