A problem in question to get a volume of a football! (calculus)?

Question

I cannnnt do this! I spent 2 hours and it is hard !
please ! help me out :p

the problem reads like this : Suppose you are asked to estimate the volume of a football. you measure and find that a football is 28 cm long. You use a piece of string and measure the circumference at its widest point to be 53cm. The circumference 7 cm from each end is 45 cm. Use Simpson's Rule to make your estimate...

Well... I just learned about Simpson's Rule. I heard there is a formula for volume using Simpson's Rule. However, I am not supposed to use that because I only learned a formula only for
area... So I have to use the one for area to get the volume..

Help me out!!

Answer 1

Use your imagination. Think outside the box, or at least outside the football. You use your Simpson rule for the area, the way it is usually used. Then you take each strip of area and you rotate it about the x axis. The arguement is that if you sliced the football with a vertical knife, and looked at each cross section, it would be circular. So you have a bunch of x values from 0 to 28 cm. For each x value, you've figured out a y value based on the description in paragraph 2. Now, each volume will be pi y^2 delta x, where delta x is the thin width of each segment in Simpson's rule. So you do this and sum the volumes.