Math worksheet for calculating the surface area of cylinders with real-world examples.

Let's solve each problem step by step, calculating the surface area of each cylinder. We’ll use the formulas for surface area depending on whether the cylinder is closed (has both top and bottom) or open (missing one or both ends).

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🔷 Formulas:

- Lateral Surface Area (side only) = $ 2\pi r h $
- Area of one circular base = $ \pi r^2 $
- Total Surface Area (closed cylinder) = $ 2\pi r h + 2\pi r^2 $
- Surface Area (open at one end) = $ 2\pi r h + \pi r^2 $
- Surface Area (open at both ends, like a pipe) = $ 2\pi r h $

> Remember:
> - Radius $ r = \frac{\text{diameter}}{2} $
> - Use $ \pi \approx 3.14 $

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## ✔ Problem 1: Hockey Puck (Closed Cylinder)

Given:
- Diameter = 3 in → Radius $ r = \frac{3}{2} = 1.5 $ in
- Height $ h = 1 $ in

This is a closed cylinder (has top and bottom).

$$
\text{SA} = 2\pi r h + 2\pi r^2
= 2\pi(1.5)(1) + 2\pi(1.5)^2
= 3\pi + 2\pi(2.25)
= 3\pi + 4.5\pi
= 7.5\pi
$$

$$
7.5 \times 3.14 = 23.55 \approx \boxed{23.6} \text{ in}^2
$$

✔ Answer: 23.6 in²

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## ✔ Problem 2: Cardboard Tube (Closed Cylinder)

Given:
- Diameter = 4 cm → $ r = 2 $ cm
- Height = 12 cm

It's a closed tube, so both ends are present.

$$
\text{SA} = 2\pi r h + 2\pi r^2
= 2\pi(2)(12) + 2\pi(2)^2
= 48\pi + 8\pi
= 56\pi
$$

$$
56 \times 3.14 = 175.84 \approx \boxed{175.8} \text{ cm}^2
$$

✔ Answer: 175.8 cm²

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## ✔ Problem 3: Plant Pot (Open Top – No Lid)

Given:
- Diameter = 12 in → $ r = 6 $ in
- Height = 17 in

No lid → only one base and lateral surface.

$$
\text{SA} = 2\pi r h + \pi r^2
= 2\pi(6)(17) + \pi(6)^2
= 204\pi + 36\pi
= 240\pi
$$

$$
240 \times 3.14 = 753.6 \approx \boxed{753.6} \text{ in}^2
$$

✔ Answer: 753.6 in²

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## ✔ Problem 4: Plastic Pipe (Open at Both Ends)

Given:
- Diameter = 14 cm → $ r = 7 $ cm
- Length = 3 m = 300 cm (convert to same unit!)

Since it's a pipe, it has no ends → only lateral surface area.

$$
\text{SA} = 2\pi r h = 2\pi(7)(300) = 4200\pi
$$

$$
4200 \times 3.14 = 13,188 \approx \boxed{13,188.0} \text{ cm}^2
$$

✔ Answer: 13,188.0 cm²

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📝 Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | 23.6 in² |
| 2) | 175.8 cm² |
| 3) | 753.6 in² |
| 4) | 13,188.0 cm² |

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