Find the volumes of the solids whose bases are bounded by the circle x^2 + y^2 = 9, with the indicated cross sections taken perpendicular to the x-axis. a) Squares

x ^2 + y ^2 = 9   =>   y = y(x) = ± √(9 - x ^2)

Each cross section would be a square with side length equal to the vertical distance between the upper and lower semicircles defined by y(x), which is

√(9 - x ^2) - (- √(9 - x ^2)) = 2 √(9 - x ^2)

The area of each square section is the square of this length,

(2 √(9 - x ^2)) = 4 (9 - x ^2) = 36 - 4x ^2

We get the whole solid for -3 ≤ x ≤ 3, so integrating gives a volume of

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above