need help on a word problem

[josh123]

A fuel storage tank is formed by attaching a hemisphere to each end of a right circular cylinder. If the cylindrical part of the tank is 50 feet long and its volume is 5022p cubic feet, find the common radius of the cylinder and the hemispheres.

I am totally clueless........ but i thought maybe the answer was 9 or 12?

 

[tkhunny]

I'm going to press you a bit on this one. It is not as hard as it may seem.

If you take the two ends and glue them together, doesn't that make a whole sphere? See if that makes it any easier.

 

[josh123]

14 sq ft? I am lost man!

 

[stapel]

The volume of a cylinder with radius r and height (or length, if sideways) h is given by:

. . . . .V_cyl. = (pi)r²h

The volume of a sphere (or two hemispheres) with radius r is given by:

. . . . .V_sphere = (4/3)(pi)r³

The volume of a cylinder with two hemispherical endcaps would be the sum of these two volumes.

You have given the length h and the total volume V. Form the sum, set equal to V, plug in the known values for h and V, and solve for r.

Hope that helps a bit. If you get stuck, please reply showing all of your work. Thank you.

Eliz.