Surface area calculation worksheet for cylinders and cones.

Sure! Let’s solve each problem step by step. We are finding the surface area of cylinders and cones.

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🔷 Important Formulas:

#### 🟢 Cylinder (Total Surface Area):
> SA = 2πr² + 2πrh = 2πr(r + h)
> - r = radius
> - h = height
> - Includes both circular bases and lateral surface.

#### 🟠 Cone (Total Surface Area):
> SA = πr² + πrℓ = πr(r + ℓ)
> - r = radius
> - ℓ = slant height (given directly in diagrams)
> - Includes base circle and lateral surface.

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## ✔ Problem-by-Problem Solutions:

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1) Cylinder: r = 8 ft, h = 12 ft

SA = 2πr(r + h)
= 2π(8)(8 + 12)
= 2π(8)(20)
= 320π
≈ 320 × 3.1416 ≈ 1005.31 ft²

✔ Answer: 1005.31 ft²

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2) Cone: r = 4 in, ℓ = 6 in

SA = πr(r + ℓ)
= π(4)(4 + 6)
= π(4)(10)
= 40π
≈ 40 × 3.1416 ≈ 125.66 in²

✔ Answer: 125.66 in²

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3) Cylinder: r = 6 yd, h = 8 yd

SA = 2πr(r + h)
= 2π(6)(6 + 8)
= 2π(6)(14)
= 168π
≈ 168 × 3.1416 ≈ 527.79 yd²

✔ Answer: 527.79 yd²

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4) Cone: r = 5 mm, ℓ = 13 mm

SA = πr(r + ℓ)
= π(5)(5 + 13)
= π(5)(18)
= 90π
≈ 90 × 3.1416 ≈ 282.74 mm²

✔ Answer: 282.74 mm²

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5) Cone: r = 6 mm, ℓ = 14 mm

SA = πr(r + ℓ)
= π(6)(6 + 14)
= π(6)(20)
= 120π
≈ 120 × 3.1416 ≈ 376.99 mm²

✔ Answer: 376.99 mm²

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6) Cylinder: r = 6 cm, h = 8 cm

SA = 2πr(r + h)
= 2π(6)(6 + 8)
= 2π(6)(14)
= 168π
≈ 168 × 3.1416 ≈ 527.79 cm²

✔ Answer: 527.79 cm²

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7) Cylinder: r = 7 yd, h = 10 yd

SA = 2πr(r + h)
= 2π(7)(7 + 10)
= 2π(7)(17)
= 238π
≈ 238 × 3.1416 ≈ 747.70 yd²

✔ Answer: 747.70 yd²

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8) Cone: r = 7 ft, ℓ = 10 ft

SA = πr(r + ℓ)
= π(7)(7 + 10)
= π(7)(17)
= 119π
≈ 119 × 3.1416 ≈ 373.85 ft²

✔ Answer: 373.85 ft²

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9) Cone: r = 4 cm, ℓ = 6 cm

SA = πr(r + ℓ)
= π(4)(4 + 6)
= π(4)(10)
= 40π
≈ 40 × 3.1416 ≈ 125.66 cm²

✔ Answer: 125.66 cm²

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## 📋 Final Answers Summary:

| Problem | Shape | Surface Area |
|---------|---------|----------------------|
| 1 | Cylinder| 1005.31 ft² |
| 2 | Cone | 125.66 in² |
| 3 | Cylinder| 527.79 yd² |
| 4 | Cone | 282.74 mm² |
| 5 | Cone | 376.99 mm² |
| 6 | Cylinder| 527.79 cm² |
| 7 | Cylinder| 747.70 yd² |
| 8 | Cone | 373.85 ft² |
| 9 | Cone | 125.66 cm² |

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✔ All answers rounded to the nearest hundredth as instructed.

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