Calculate the area of each cone using the given dimensions.

Actually, there's an important clarification needed here.

The worksheet is titled “Area Of A Cone”, but in geometry, we typically calculate the surface area or volume of a 3D shape like a cone — not just “area,” which usually refers to 2D shapes.

Looking at the dimensions given (height and diameter), and since the worksheet asks for “Area,” it’s most likely referring to the total surface area of the cone (which includes the base circle and the curved lateral surface).

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🔷 Formula for Total Surface Area of a Cone:

> Total Surface Area = πr² + πrℓ

Where:
- r = radius of the base
- ℓ = slant height (the distance from the tip of the cone to the edge of the base)
- πr² = area of the circular base
- πrℓ = lateral (curved) surface area

But wait — the worksheet gives height (h) and diameter (d), not the slant height (ℓ).

So we need to first calculate the slant height using the Pythagorean theorem:

> ℓ = √(r² + h²)

Then plug into the surface area formula.

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Let’s solve each cone one by one.

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## 🔹 Cone 1: Height = 11, Diameter = 9 → Radius r = 4.5

Step 1: Find slant height ℓ

ℓ = √(r² + h²) = √(4.5² + 11²) = √(20.25 + 121) = √141.25 ≈ 11.885

Step 2: Total Surface Area

= πr² + πrℓ
= π(4.5)² + π(4.5)(11.885)
= π(20.25) + π(53.4825)
= π(73.7325)
≈ 231.63 (using π ≈ 3.1416)

✔ Answer: ≈ 231.63

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## 🔹 Cone 2: Height = 4, Diameter = 7 → Radius r = 3.5

ℓ = √(3.5² + 4²) = √(12.25 + 16) = √28.25 ≈ 5.315

Surface Area = π(3.5)² + π(3.5)(5.315)
= π(12.25) + π(18.6025)
= π(30.8525)
≈ 96.93

✔ Answer: ≈ 96.93

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## 🔹 Cone 3: Height = 3, Diameter = 1 → Radius r = 0.5

ℓ = √(0.5² + 3²) = √(0.25 + 9) = √9.25 ≈ 3.041

Surface Area = π(0.5)² + π(0.5)(3.041)
= π(0.25) + π(1.5205)
= π(1.7705)
≈ 5.56

✔ Answer: ≈ 5.56

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## 🔹 Cone 4: Height = 12, Diameter = 5 → Radius r = 2.5

ℓ = √(2.5² + 12²) = √(6.25 + 144) = √150.25 ≈ 12.258

Surface Area = π(2.5)² + π(2.5)(12.258)
= π(6.25) + π(30.645)
= π(36.895)
≈ 115.91

✔ Answer: ≈ 115.91

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## 🔹 Cone 5: Height = 6, Diameter = 5 → Radius r = 2.5

ℓ = √(2.5² + 6²) = √(6.25 + 36) = √42.25 = 6.5 (exact!)

Surface Area = π(2.5)² + π(2.5)(6.5)
= π(6.25) + π(16.25)
= π(22.5)
= 70.686 (since 22.5 × π ≈ 70.686)

✔ Answer: ≈ 70.69

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## 🔹 Cone 6: Height = 10, Diameter = 4 → Radius r = 2

ℓ = √(2² + 10²) = √(4 + 100) = √104 ≈ 10.198

Surface Area = π(2)² + π(2)(10.198)
= π(4) + π(20.396)
= π(24.396)
≈ 76.64

✔ Answer: ≈ 76.64

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## ✔ Final Answers (Rounded to 2 decimal places):

| Cone | Area (Total Surface Area) |
|------|---------------------------|
| 1 | 231.63 |
| 2 | 96.93 |
| 3 | 5.56 |
| 4 | 115.91 |
| 5 | 70.69 |
| 6 | 76.64 |

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📌 Note: If your teacher meant volume instead of surface area, the formula would be V = (1/3)πr²h — but given the context and the inclusion of slant height calculations implied by the diagram (even if not labeled), surface area is the correct interpretation.

Let me know if you want the volume answers too!