Question

Let R be the region in the first quadrant bounded by the graph of y=x, the vertical line x = 9, and the x-axis, as shown in the figure.

a) Write, then evaluate (show all of your work), an integral expression that gives the volume of the solid generated when R is rotated about the x-axis.
b) Write, then evaluate (show all of your work), an integral expression that gives the volume of the solid generated when R is rotated about the vertical line x = 9.

Answer 1

The volume of the solid generated when R is revolved about the

x

-axis is

848

15

π

or approximately

177.6

.

The area of a circle with a radius equal to

8

−

x

3

2

at any given

x

is

π

⋅

(

8

−

x

3

2

)

2

.

= 848

15

π

≈

177.6