Absolutely! Let’s solve each problem step by step. We’ll use the
formula for the volume of a sphere:
>
V = (4/3)πr³
Where:
-
V is the volume,
-
r is the radius of the sphere,
-
π ≈ 3.14159 (we’ll use this value for accuracy, then round final answers to 2 decimal places).
---
🔹 Problem 1:
Given: Radius = 2¼ m =
2.25 m
Working Out:
V = (4/3) × π × (2.25)³
First, calculate 2.25³:
2.25 × 2.25 = 5.0625
5.0625 × 2.25 =
11.390625
Now multiply:
(4/3) × π × 11.390625
= (4 × π × 11.390625) ÷ 3
≈ (4 × 3.14159 × 11.390625) ÷ 3
≈ (143.138) ÷ 3
≈
47.7127
Volume = 47.71 m³ (rounded to 2 decimal places)
---
🔹 Problem 2:
Given: Diameter = 14 cm → So
radius = 14 ÷ 2 = 7 cm
Working Out:
V = (4/3) × π × (7)³
7³ = 343
V = (4/3) × π × 343
= (4 × π × 343) ÷ 3
≈ (4 × 3.14159 × 343) ÷ 3
≈ (4309.75) ÷ 3
≈
1436.58
Volume = 1436.58 cm³
---
🔹 Problem 3:
Given: Diameter = 3.2 in → So
radius = 3.2 ÷ 2 = 1.6 in
Working Out:
V = (4/3) × π × (1.6)³
1.6³ = 1.6 × 1.6 = 2.56; 2.56 × 1.6 =
4.096
V = (4/3) × π × 4.096
≈ (4 × 3.14159 × 4.096) ÷ 3
≈ (51.47) ÷ 3
≈
17.16
Volume = 17.16 in³
---
🔹 Problem 4:
Given: Radius = 12 ft
Working Out:
V = (4/3) × π × (12)³
12³ = 1728
V = (4/3) × π × 1728
= (4 × π × 1728) ÷ 3
≈ (4 × 3.14159 × 1728) ÷ 3
≈ (21714.69) ÷ 3
≈
7238.23
Volume = 7238.23 ft³
---
🔹 Problem 5:
Given: Diameter = 16.4 cm → So
radius = 16.4 ÷ 2 = 8.2 cm
Working Out:
V = (4/3) × π × (8.2)³
8.2³ = 8.2 × 8.2 = 67.24; 67.24 × 8.2 =
551.368
V = (4/3) × π × 551.368
≈ (4 × 3.14159 × 551.368) ÷ 3
≈ (6928.38) ÷ 3
≈
2309.46
Volume = 2309.46 cm³
---
##
✔ Final Answers Table:
| SPHERE | WORKING OUT | VOLUME |
|--------|--------------------------------------------------|---------------|
| 1) | V = (4/3)π(2.25)³ ≈ 47.71 |
47.71 m³ |
| 2) | V = (4/3)π(7)³ ≈ 1436.58 |
1436.58 cm³ |
| 3) | V = (4/3)π(1.6)³ ≈ 17.16 |
17.16 in³ |
| 4) | V = (4/3)π(12)³ ≈ 7238.23 |
7238.23 ft³ |
| 5) | V = (4/3)π(8.2)³ ≈ 2309.46 |
2309.46 cm³ |
---
✔ All answers are rounded to
2 decimal places as requested.
Let me know if you’d like to see the calculations with fractions or using calculator steps!
Parent Tip: Review the logic above to help your child master the concept of volume of a sphere word problems worksheet.
