# Describe the solid whose volume is represented by int_(0)^(3) (2pi x^5)dx. ?

## please do this question. Thank you.

##### 1 Answer
Jul 8, 2017

Recall that a solid of revolution about the $y$ axis is given in general for the shell method by

$V = 2 \pi {\int}_{a}^{b} x r \left(x\right) \mathrm{dx}$,

where $r \left(x\right)$ describes the shape that will be revolved around a vertical axis, $x$ indicates the distance of the function's edge to the rotational origin, and $2 \pi$ is the circumference in radians.

In this case, you have $r \left(x\right) = {x}^{4}$ from $x = 0 \to 3$.

I assume it is rotated about $x = 0$. If so, it is going to look like a cylinder with an upside-down-silo-shaped hole.