What is the surface area of a sphere if its volume is 288π cubic inches? leave your answers in terms of π. a. 216π in² b. 144π in² c. 288π in² d. 16π in²

Remark

The Volume of a sphere is V = (4/3) pi r^3. From that, you need to find r.

Givens

V = 288*pi

Substitute

288 pi = (4/3) pi r^3 Divide both sides by pi

288 pi/pi = (4/3) pi r^3 / pi

288 = (4/3) r^3 Multiply by 3

288*3 = 4*r^3

864 = 4r^3 Divide by 4

864 / 4 = 4 r^3 / 4

216 = r^3

Take the cube root of both sides.

cube_root(r^3) = cube_root(216)

r = 6

Surface Area

Formula

Area = 4 pi r^2

Substitute

r = 6

Area = 4 * pi * 6^2

Area = 4*36 * pi

Area = 144 pi Answer

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068