L28 · Volume of cylinders, cones, and spheres

1. 1.

   A cylinder has radius 6 cm and height 9 cm. Volume in terms of π?

   Answer. 324π cubic cm

   V = πr²h = π(6)²(9) = 324π.

2. 2.

   A cone has radius 2 cm and height 6 cm. Volume in terms of π?

   Answer. 8π cubic cm

   V = (13)πr²h = (13)π(4)(6) = 8π.

3. 3.

   A sphere has radius 4 cm. Volume in terms of π?

   Answer. 8513π cubic cm

   V = (43)πr³ = (43)π(64) = 8513π.

4. 4.

   A cylinder has radius 3 cm and height 9 cm. Volume in terms of π?

   Answer. 81π cubic cm

   V = πr²h = π(3)²(9) = 81π.

5. 5.

   A cone has radius 3 cm and height 7 cm. Volume in terms of π? Write a complete answer — Nora will compare with a partner.

   Answer. 21π cubic cm

   V = (13)πr²h = (13)π(9)(7) = 21π.

6. 6.

   A sphere has radius 3 cm. Volume in terms of π? Write a complete answer — Jonah will compare with a partner.

   Answer. 36π cubic cm

   V = (43)πr³ = (43)π(27) = 36π.

7. 7.

   A cylinder has radius 6 cm and height 4 cm. Volume in terms of π? Write a complete answer — Jonah will compare with a partner.

   Answer. 144π cubic cm

   V = πr²h = π(6)²(4) = 144π.

8. 8.

   A cone has radius 6 cm and height 3 cm. Volume in terms of π? Write a complete answer — Malik will compare with a partner.

   Answer. 36π cubic cm

   V = (13)πr²h = (13)π(36)(3) = 36π.

9. 9.

   A sphere has radius 3 cm. Volume in terms of π? Write a complete answer — Owen will compare with a partner.

   Answer. 36π cubic cm

   V = (43)πr³ = (43)π(27) = 36π.

10. 10.

    A cylinder has radius 2 cm and height 7 cm. Volume in terms of π? Write a complete answer — Elena will compare with a partner.

    Answer. 28π cubic cm

    V = πr²h = π(2)²(7) = 28π.

11. 11.

    Think

    Nora tried this problem:
    A cone has radius 5 cm and height 8 cm. Volume in terms of π?
    Nora wrote 6624π cubic cm. That is not correct. What is the right answer?

    Answer. 6623π cubic cm

    Nora’s answer 6624π cubic cm is off. V = (13)πr²h = (13)π(25)(8) = 6623π.

12. 12.

    Think

    Jonah tried this problem:
    A sphere has radius 2 cm. Volume in terms of π?
    Jonah wrote 1024π cubic cm. That is not correct. What is the right answer?

    Answer. 1023π cubic cm

    Jonah’s answer 1024π cubic cm is off. V = (43)πr³ = (43)π(8) = 1023π.

Original extra practice. Keys are computed from the items, not guessed.