Let's solve each of the volume problems using the appropriate formulas. We'll use:
-
Volume of a Sphere:
$$
V = \frac{4}{3} \pi r^3
$$
-
Volume of a Cylinder:
$$
V = \pi r^2 h
$$
-
Volume of a Cone:
$$
V = \frac{1}{3} \pi r^2 h
$$
We’ll use $\pi \approx 3.1416$, and round all answers to the nearest
tenth (one decimal place).
---
1. Sphere (Top Left)
- Radius $ r = 10.7 $
$$
V = \frac{4}{3} \pi (10.7)^3 = \frac{4}{3} \pi (1225.043) \approx \frac{4}{3} \times 3.1416 \times 1225.043
$$
$$
\approx 4.1888 \times 1225.043 \approx 5130.9
$$
✔ Answer: $ V = 5130.9 $ units³
---
2. Cylinder (Top Right)
- Radius $ r = 9.2 $, Height $ h = 14 $
$$
V = \pi r^2 h = \pi (9.2)^2 (14) = \pi (84.64)(14) = \pi (1184.96)
$$
$$
\approx 3.1416 \times 1184.96 \approx 3723.5
$$
✔ Answer: $ V = 3723.5 $ units³
---
3. Sphere (Middle Left)
- Radius $ r = 6.8 $
$$
V = \frac{4}{3} \pi (6.8)^3 = \frac{4}{3} \pi (314.432) \approx \frac{4}{3} \times 3.1416 \times 314.432
$$
$$
\approx 4.1888 \times 314.432 \approx 1318.4
$$
✔ Answer: $ V = 1318.4 $ units³
---
4. Cone (Middle Right)
- Radius $ r = 17.7 $, Height $ h = 15.7 $
$$
V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (17.7)^2 (15.7)
$$
First: $ (17.7)^2 = 313.29 $
Then: $ 313.29 \times 15.7 = 4923.553 $
Now: $ \frac{1}{3} \times 3.1416 \times 4923.553 \approx 1.0472 \times 4923.553 \approx 5154.9 $
✔ Answer: $ V = 5154.9 $ units³
---
5. Cone (Bottom Left)
- Radius $ r = 5.6 $, Height $ h = 14 $
$$
V = \frac{1}{3} \pi (5.6)^2 (14) = \frac{1}{3} \pi (31.36)(14) = \frac{1}{3} \pi (439.04)
$$
$$
\approx \frac{1}{3} \times 3.1416 \times 439.04 \approx 1.0472 \times 439.04 \approx 459.5
$$
✔ Answer: $ V = 459.5 $ units³
---
6. Cylinder (Bottom Right)
- Radius $ r = 5.1 $, Height $ h = 14 $
$$
V = \pi r^2 h = \pi (5.1)^2 (14) = \pi (26.01)(14) = \pi (364.14)
$$
$$
\approx 3.1416 \times 364.14 \approx 1144.5
$$
✔ Answer: $ V = 1144.5 $ units³
---
✔ Final Answers (Rounded to Nearest Tenth):
| Shape | Volume (units³) |
|-----------|------------------|
| Sphere | 5130.9 |
| Cylinder | 3723.5 |
| Sphere | 1318.4 |
| Cone | 5154.9 |
| Cone | 459.5 |
| Cylinder | 1144.5 |
Let me know if you'd like these written in the boxes on the worksheet!
Parent Tip: Review the logic above to help your child master the concept of volume of cylinder cones and spheres worksheet.
