Final Answer:
1. Formula: $ V = \pi r^2 h $
Plug in values: $ V = 3.14 \times (2)^2 \times 7 = 3.14 \times 4 \times 7 = 87.92 $
Volume:
87.92 in³
2. Formula: $ V = \frac{1}{3} \pi r^2 h $
Plug in values: $ V = \frac{1}{3} \times 3.14 \times (4)^2 \times 6 = \frac{1}{3} \times 3.14 \times 16 \times 6 = \frac{1}{3} \times 301.44 = 100.48 $
Volume:
100.48 in³
3. Formula: $ V = \frac{4}{3} \pi r^3 $
Plug in values: $ V = \frac{4}{3} \times 3.14 \times (3)^3 = \frac{4}{3} \times 3.14 \times 27 = \frac{4}{3} \times 84.78 = 113.04 $
Volume:
113.04 in³
4. Formula: $ V = \pi r^2 h $
Radius = $ \frac{6}{2} = 3 $ in
Plug in values: $ V = 3.14 \times (3)^2 \times 10 = 3.14 \times 9 \times 10 = 282.6 $
Volume:
282.6 in³
5. Formula: $ V = \frac{1}{3} \pi r^2 h $
Radius = $ \frac{4}{2} = 2 $ in
Plug in values: $ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 3 = \frac{1}{3} \times 3.14 \times 4 \times 3 = \frac{1}{3} \times 37.68 = 12.56 $
Volume:
12.56 in³
6. Formula: $ V = \frac{4}{3} \pi r^3 $
Radius = $ \frac{4}{2} = 2 $ in
Plug in values: $ V = \frac{4}{3} \times 3.14 \times (2)^3 = \frac{4}{3} \times 3.14 \times 8 = \frac{4}{3} \times 25.12 = 33.49 $ (rounded to nearest hundredth)
Volume:
33.49 in³
7. Given: $ V = 288\pi $ in³, $ h = 6 $ in
Use $ V = \pi r^2 h $ → $ 288\pi = \pi r^2 \cdot 6 $
Divide both sides by $ \pi $: $ 288 = 6r^2 $
$ r^2 = 48 $ → $ r = \sqrt{48} = 4\sqrt{3} \approx 6.93 $ in
Radius:
≈ 6.93 in
8. Given: $ V = 44 $ in³, base area = $ 33 $ in²
For a cone: $ V = \frac{1}{3} \times \text{base area} \times h $
$ 44 = \frac{1}{3} \times 33 \times h $ → $ 44 = 11h $ → $ h = 4 $ in
Height:
4 in
9. Given: $ V = 36\pi $ in³
Use sphere formula: $ V = \frac{4}{3} \pi r^3 $
$ 36\pi = \frac{4}{3} \pi r^3 $
Cancel $ \pi $: $ 36 = \frac{4}{3} r^3 $
Multiply both sides by $ \frac{3}{4} $: $ r^3 = 27 $ → $ r = 3 $ in
Radius:
3 in
Parent Tip: Review the logic above to help your child master the concept of worksheet volume of cones cylinder and spheres answers.
