#### To determine

**To find:**

The volume generated by rotating the region R2 about the line OC by using the figure.

#### Answer

V=π9

#### Explanation

**1) Concept:**

i. If the cross section is a disc and the radius of the disc is in terms of x or y then the area is A=π radius2

ii. The volume of the solid revolution about the y-axis is

V= ∫abA(y)dy

**2) Given:**

**Figure:**

**3) Calculation:**

Here, the line OC appears to be the line x=0.

Rotating R2 about the OC, that is, the line x=0, so the cross section is perpendicular to the y-axis and it is a disc with the radius r=y4 because it is the distance from the curve y= x4 to the axis of rotation line OC (x=0)

From the figure, the solid lies between y=0 and y=1.

By using the concept,

V= ∫01πy42 dy

V=∫01πy8 dy

After integrating,

V= πy9910

V=π19-0=π9

The volume generated by rotating the region R2 about the line OC is

V=π9

**Conclusion:**

The volume generated by rotating the region R2 about the line OC is

V=π9