# How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y=x^2#, x = 2, x = 7, y = 0 revolved about the x=8?

##### 1 Answer

Dec 15, 2017

#### Explanation:

shell method: volume =

In this problem,

r is the distance from a certain x value in the interval [2,7] to the axis of rotation, which is x=8. Since r must be a positive distance, it is

h is the height of each shell (parallel to axis of rotation). in this case it is the distance between the upper and lower bounds of the region, or

plugging in: volume =

simplify: