Question

A graphing calculator is recommended. A grain silo consists of a cylindrical main section and a hemispherical roof. If the total volume of the silo (including the part inside the roof section) is 15,000 ft3 and the cylindrical part is 30 ft tall, what is the radius of the silo, correct to the nearest tenth of a foot

Answer 1

11.28 ft

Explanation:

The volume of a cylinder can be written as;

Volume V1 = πr^2 h

The volume of an hemisphere can be written as;

Volume V2 = (2/3)πr^3

The total volume of the silo is;

V = V1 + V2

V = πr^2 h + (2/3)πr^3

Given;

Volume of silo V= 15000 ft^3

Height of cylinder part h = 30 ft

Substituting the values;

V = πr^2 h + (2/3)πr^3

15000 = 30πr^2 + (2/3)πr^3

15000/π = 30r^2 + (2/3)r^3

2r^3 + 90r^2 - (15000×3/π) = 0

Solving the equation, we have;

r = 11.28 ft or -15.61 ft or -40.67 ft

Since the radius cannot be negative;

Radius r = 11.28 ft