Absolutely! Let’s solve each of the 6 cylinder volume problems step by step, using the formula:
>
V = π × r² × h
Where:
-
V = Volume
-
π ≈ 3.14 (as instructed)
-
r = radius of the circular base
-
h = height of the cylinder
We’ll round each final answer to the
nearest tenth.
---
🔹 Problem 1:
- Radius (r) =
5 mm
- Height (h) =
6 mm
Calculation:
V = 3.14 × (5)² × 6
V = 3.14 × 25 × 6
V = 3.14 × 150
V =
471.0 mm³
✔ Answer: 471.0 mm³
---
🔹 Problem 2:
- Radius (r) =
3 m
- Height (h) =
6 m
Calculation:
V = 3.14 × (3)² × 6
V = 3.14 × 9 × 6
V = 3.14 × 54
V =
169.56 → rounded to 169.6 m³
✔ Answer: 169.6 m³
---
🔹 Problem 3:
- Radius (r) =
3 cm
- Height (h) =
9 cm
Calculation:
V = 3.14 × (3)² × 9
V = 3.14 × 9 × 9
V = 3.14 × 81
V =
254.34 → rounded to 254.3 cm³
✔ Answer: 254.3 cm³
---
🔹 Problem 4:
- Radius (r) =
5 cm
- Height (h) =
12 cm
Calculation:
V = 3.14 × (5)² × 12
V = 3.14 × 25 × 12
V = 3.14 × 300
V =
942.0 cm³
✔ Answer: 942.0 cm³
---
🔹 Problem 5:
- Radius (r) =
7 mm
- Height (h) =
8 mm
Calculation:
V = 3.14 × (7)² × 8
V = 3.14 × 49 × 8
V = 3.14 × 392
V =
1230.88 → rounded to 1230.9 mm³
✔ Answer: 1230.9 mm³
---
🔹 Problem 6:
- Radius (r) =
1 m
- Height (h) =
10 m
Calculation:
V = 3.14 × (1)² × 10
V = 3.14 × 1 × 10
V =
31.4 m³
✔ Answer: 31.4 m³
---
##
✔ Final Answers Summary:
1.
471.0 mm³
2.
169.6 m³
3.
254.3 cm³
4.
942.0 cm³
5.
1230.9 mm³
6.
31.4 m³
---
## 💡 Explanation Recap:
The volume of a cylinder is found by multiplying the area of its circular base (πr²) by its height (h). This makes intuitive sense — imagine stacking many thin circular disks (each with area πr²) on top of each other to a height h. The total space they occupy is the volume.
Always double-check:
- You’re using
radius, not diameter.
- Units are consistent.
- Round
only at the end to avoid rounding errors.
Let me know if you’d like to visualize any of these or see the steps broken down further!
Parent Tip: Review the logic above to help your child master the concept of volume cylinder worksheet.
