Question 348648
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]