# How do you find the volume of the solid generated by revolving the region bounded by the curves y = 10 / x², y = 0, x = 1, x = 5 rotated about the y-axis?

##### 1 Answer

#### Explanation:

Integrate by Method of Rings

Solution:

(1) Determine the plot of

(2) In this solution, the positive side of the curve was used (so as not to deal with negative signs ^_^).

(3) Since the curve is to be rotated about the y-axis, the cross section of the solid should be perpendicular to the y-axis and has its area a function of y.

(4) Since the curve is to be bounded from x=1, the **inner radius** of the ring or the distance of the line x=1 to the axis of rotation (which is x=0) **is equal to 1** .

(5) As for the **outer radius** of the ring, the distance of the curve to the axis of rotation **is expressed as #x=sqrt(10/y)#**

(6) Hence the area of the ring is,

(7) If we take a differential element, dy, multiply it to the cross sectional area, then integrate it, we get the volume of the solid. As for the limits of integration, find the values of y at x = 1 and x = 5 based on the curve

(8) Determining the volume,

(9)