Question

How do you find the volume of the solid `y=4-x^2` revolved about the x-axis?

Answer 1

Use the disc method. The volume is `107.233`.

Explanation:

First, set `y` equal to `0` to find the bounds.

`0=4-x^2`
`x^2=4`
`x in {-2,2}`

So our bounds are `-2` and `2`.

Next, use the disc method to find the volume (`y = r`).

`int_-2^2piy^2 dx = piint_-2^2(4-x^2)^2dx`

`= piint_-2^2(16-8x^2+x^4)dx`

`= pi [16x-8/3x^3+x^5/5]_-2^2`

`= pi (32-64/3+32/5)-pi(-32+64/3-32/5)`

`=512/15pi`

`=107.233`

Final Answer