Absolutely! Let’s solve each cone volume problem step by step using the formula for the
volume of a cone:
>
V = (1/3) × π × r² × h
Where:
-
V = volume
-
r = radius of the base
-
h = height of the cone
-
π ≈ 3.14159 (we’ll use 3.142 for calculation unless specified)
We’ll calculate each one, show the working, and round the final answer to
1 decimal place as instructed.
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🔹 Problem 1:
Radius = 3 cm,
Height = 8 cm
Working Out:
V = (1/3) × π × (3)² × 8
= (1/3) × π × 9 × 8
= (1/3) × π × 72
= 24 × π
≈ 24 × 3.142
≈
75.408
✔ Volume = 75.4 cm³
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🔹 Problem 2:
Radius = 1½ ft = 1.5 ft,
Height = 3 ft
Working Out:
V = (1/3) × π × (1.5)² × 3
= (1/3) × π × 2.25 × 3
= (1/3) × π × 6.75
= 2.25 × π
≈ 2.25 × 3.142
≈
7.0695
✔ Volume = 7.1 ft³
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🔹 Problem 3:
Radius = 4.2 m,
Height = 6 m
Working Out:
V = (1/3) × π × (4.2)² × 6
= (1/3) × π × 17.64 × 6
= (1/3) × π × 105.84
= 35.28 × π
≈ 35.28 × 3.142
≈
110.83
✔ Volume = 110.8 m³
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🔹 Problem 4:
Radius = 4¾ in = 4.75 in,
Height = 8½ in = 8.5 in
Working Out:
V = (1/3) × π × (4.75)² × 8.5
First, 4.75² = 22.5625
Then, 22.5625 × 8.5 = 191.78125
Then, (1/3) × 191.78125 = 63.927083...
Then, × π ≈ 63.927083 × 3.142 ≈
200.83
✔ Volume = 200.8 in³
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🔹 Problem 5:
Radius = 5 cm,
Height = 18 cm
Working Out:
V = (1/3) × π × (5)² × 18
= (1/3) × π × 25 × 18
= (1/3) × π × 450
= 150 × π
≈ 150 × 3.142
≈
471.3
✔ Volume = 471.3 cm³
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##
✔ Final Answers Summary:
| # | Working Out | Volume |
|---|-----------------------------------------------------------------------------|------------|
| 1 | V = (1/3) × π × 3² × 8 = 24π ≈ 75.4 |
75.4 cm³ |
| 2 | V = (1/3) × π × (1.5)² × 3 = 2.25π ≈ 7.1 |
7.1 ft³ |
| 3 | V = (1/3) × π × (4.2)² × 6 = 35.28π ≈ 110.8 |
110.8 m³ |
| 4 | V = (1/3) × π × (4.75)² × 8.5 ≈ 63.927 × π ≈ 200.8 |
200.8 in³ |
| 5 | V = (1/3) × π × 5² × 18 = 150π ≈ 471.3 |
471.3 cm³ |
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Let me know if you’d like to see the answers formatted for printing or need help with the next worksheet! 😊
Parent Tip: Review the logic above to help your child master the concept of volume of a cone worksheet.
