Question

How do you find the volume of the solid generated when the regions bounded by the graphs of the given equations `y = root3x`, x = 0, x = 8 and the x-axis are rotated about the x-axis?

Answer 1

`96/5pi`

Explanation:

Rotation about `x` axis, hence `piinty^2dx`

`y^2 = (x^(1/3))^2 = x^(2/3)`

`=piint_0^8x^(2/3)dx`
`= [3/5x^(5/3)]_0^8`
`= 3/5pi((8/5)^(5/3)-0^(5/3))`
`= 96/5pi`