Question

What is the volume of the solid produced by revolving `f(x)=7-x, x in [0,2]`around the x-axis?

Answer 1

`V = (218pi)/3`
`\ \ \ ~~ 228.289`

Explanation:

graph{7-x [-10.29, 9.71, -1.88, 8.12]}

`y=7-x` is a straight line; The volume of revolution is that of a large cone of radius `7` height `7` minus that of smaller cone radius `5` height `5`; Using `V_("cone") = 1/3pir^2h`, Then:

`V = 1/3pi(7)^2(7) - 1/3pi(5)^2(5)`
`\ \ \ = 1/3pi(7^3-5^3)`
`\ \ \ = 1/3pi(343-125)`

`\ \ \ = (218pi)/3`
`\ \ \ ~~ 228.289`