A storage tank for propane gas is to be constructed in the shape of a right circular cylinder of altitude 30 feet with a hemisphere attached to each end.

Question

Determine the radius x so that the resulting volume is 306π ft3.

Answer 1

Say,

The radius=x Ft

Volume=4*pi*x^2+pi*(x^2)*30

           =34*pi*x^2=306*pi

x^2=306/34

      =9

x=3 Ft

 

Radius = 3 ft 

Answer 2

Hey Colsten,

 

V (circular cylinder) = Area of circle * height

 

V (sphere) = (4/3) π (r³) = (4/3) π (x³)

 

Total volume is: (4/3) π (x³)+ π (x²) h = 306π

 

(cancel the pi from both sides):

 

(4/3) x³ + x² h = 306  -->  (4/3) x³ + x² (30) = 306

 

(4/3) x³ + 30x² = 306

 

4x³ + 90x² = 918

 

2x³ + 45x2 = 459

 

2x³ + 45x² -459 = 0

 

(use synthetic division)  (let's try 3)

 

3   _   2   45     0      -459

                6    153     459

         2    51   153       0

 

So, r = 3 ft.  (2, 51, 153) is written as 2x² + 51x + 153 = 0.  I've also tried synthetic division once more with (51 , 3) & (17 , 9) the factors of 153 but it didn't work.  Therefore, this quadratic is not factorable.

 

In factored form, you will have (x - 3) (2x² + 51x +153) = 0

 

In conclusion, the radius of storage tank must be 3 ft.

 

Sorry for missing the hemisphere part at first.  But this time around, I hope you understand how I did it.