SOLUTION: Please help! Two designs for and oil storage tank are being considered: spherical and cylindrical. The two tanks would have the same capacity and would each have an inside diamet

Click here to see ALL problems on Geometry Word Problems

Question 106906: Please help!
Two designs for and oil storage tank are being considered: spherical and cylindrical. The two tanks would have the same capacity and would each have an inside diameter of 60 feet.
a)what would be the height of the cylindrical tank?
b) If one cubic foot holds 7.5 gallons of oil, what is the capacity of each tank in gallons?
c)Which of the two designs has the smallest surface area and would thus require less material in its construction?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Two designs for and oil storage tank are being considered: spherical and cylindrical. The two tanks would have the same capacity and would each have an inside diameter of 60 feet.
:
a)what would be the height of the cylindrical tank?
r = 30 ft
Cylinder Vol = Sphere Vol
=
=
Multiply both sides by 3:
=
Divide both sides by and you have:
3h = 4*30
h = 120/3
h = 40 ft is the height of the cylinder
:
You can check this by finding the volume of both, see if they equal 113,097.3 cu/ft
:
b) If one cubic foot holds 7.5 gallons of oil, what is the capacity of each tank in gallons?
113097.3 * 7.5 = 848,230 gal
:
c)Which of the two designs has the smallest surface area and would thus require less material in its construction?
Sphere would have the smallest surface area
Sphere:
= 11,309.7 sq ft
Cylinder:
+ = 13,194.7 sq ft
:
Did this make sense to you?