Help please with Word Problem Question?

Question

A gas tank has ends that are hemispheres of radius r feet. The cylindrical midsection is 6ft long. Express the volume of the tank as a function of r.

Thanks for any help on this one.

Answer 1

Consider it as two (or possibly three) parts

First, one end, this is a hemisphere, with radius r => volume?
Secondly, a cylinder, with radius r and length 6 => volume?
Thirdly a second hemisphere as before (if it's any easier, you can combine parts 1 and 3 to generate a sphere with radius r)

Answer 2

Divide the tank into three parts: two hemispheres of equal radius which froms a sphere of radius r and a center cylinder of radius r and length 6'.
Volume cylinder = area x length = pi(r^2) x 6 = 6pi(r^2)
Volume of sphere = (4pi/3)(r^3)
Combining = 6pi(r^2) + (4pi/3)(r^3) = (r^2)(6pi + (4pi/3)r)

Answer 3

So if you chop off the two hemisphere ends and slap them together you have one sphere and you still have the 6 ft long cylinder with cross sectional area of 2pi*r^2.

If you can't take it from there, you are probably a high school student trying to get someone else to do his homework for him. So this is where I stop.

Answer 4

Volume of a hemisphere: V = 4/3 x pi x r3
Volume of a Cylinder: V = L × pi × r2,

You have 2 ends and the center.

You can do it.......................

Answer 5

V = pi x r^2 x 6 + (4/3)pi x r^3