The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the x-axis are semi-circles. What is the volume, in cubic units, of the solid?

Step-by-step explanation:

Given that the base of a solid is the circle and Cross sections of the solid perpendicular to the x-axis are semi-circles.

We know that the cross sections are semicircles with the diameter in the given circle

That is we have to find the formula for the area of any semicircle perpendicular to x-axis, and integrate it from -3 to 3.

Now the area of a semicircle is

cubic units

Let r = y  and

Then area of the semicircle crossing the x-axis at x is  given by

cubic units

 Now we can find the definite integral of A(x) from x = -3 to x = 3.

Since A(x) is an EVEN function then the definite integral of A(x) from x = -3 to x = 3 is the same as twice the integral of A(x) from x = 0 to x = 3.

We have that