A propane tank has the shape of a circular cylinder with a hemisphere at each end. The cylinder is 6 feet long and the volume of the tank is cubic feet. Find, to the nearest thousandth of a foot, the length of the radius x.
A) ft
B) ft
C) ft
D)1.041 ft
E) ft

Question

A propane tank has the shape of a circular cylinder with a hemisphere at each end. The cylinder is 6 feet long and the volume of the tank is  cubic feet. Find, to the nearest thousandth of a foot, the length of the radius x. 
A) ft 
B) ft 
C) ft 
D)1.041 ft 
E) ft

Quizplus · Accepted Answer

The volume of the propane tank is the sum of the volume of the cylinder and the two hemispheres.
Let x be the length of the radius of the cylinder and the hemisphere.
Thus,
Volume of cylinder: πx^2(6)
Volume of hemisphere: (2/3)πx^3

Total Volume = Volume of cylinder + Volume of hemisphere 1 + Volume of hemisphere 2 = 11
πx^2(6)+2(2/3)πx^3=11
6πx^2+ 4πx^3=11
4πx^3 + 6πx^2 -11=0 
Using the Newton-Raphson method, x = 1.041
Therefore, the length of the radius x is approximately 1.041 feet, which is closest to choice D.

A Propane Tank Has the Shape of a Circular Cylinder