Surface Area of Cylinders Worksheet or Mini Breakout - Free Printable

Let’s solve each cylinder’s total surface area step by step.

We are told to use π = 3.14 and round the final answer to the nearest whole number.

The formula for the total surface area of a cylinder is:

> SA = 2πr² + 2πrh

Where:
- r = radius
- h = height (or length, if lying on its side)
- The first part (2πr²) is the area of the two circular ends.
- The second part (2πrh) is the area of the curved side (like unrolling it into a rectangle).

Sometimes we’re given diameter instead of radius — remember:
> radius = diameter ÷ 2

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Problem 1:

Cylinder with:
- Diameter = 8 in → so radius r = 8 ÷ 2 = 4 in
- Height h = 2 in

SA = 2 × 3.14 × (4)² + 2 × 3.14 × 4 × 2
= 2 × 3.14 × 16 + 2 × 3.14 × 8
= 6.28 × 16 + 6.28 × 8
= 100.48 + 50.24
= 150.72

Round to nearest whole number → 151

✔ Answer 1: 151

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Problem 2:

Cylinder lying on its side:
- Radius r = 3.5 in (given directly)
- Length (height) h = 5 in

SA = 2 × 3.14 × (3.5)² + 2 × 3.14 × 3.5 × 5
First, (3.5)² = 12.25

So:
= 2 × 3.14 × 12.25 + 2 × 3.14 × 17.5
= 6.28 × 12.25 + 6.28 × 17.5
Calculate each:

6.28 × 12.25 = let’s compute:
6 × 12.25 = 73.5
0.28 × 12.25 = 3.43
→ Total = 73.5 + 3.43 = 76.93

6.28 × 17.5 =
6 × 17.5 = 105
0.28 × 17.5 = 4.9
→ Total = 105 + 4.9 = 109.9

Add them: 76.93 + 109.9 = 186.83

Round → 187

✔ Answer 2: 187

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Problem 3:

Cylinder tilted:
- Diameter = 4 in → radius r = 4 ÷ 2 = 2 in
- Height h = 2.25 in

SA = 2 × 3.14 × (2)² + 2 × 3.14 × 2 × 2.25
= 2 × 3.14 × 4 + 2 × 3.14 × 4.5
= 6.28 × 4 + 6.28 × 4.5
= 25.12 + 28.26
= 53.38

Round → 53

✔ Answer 3: 53

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Problem 4:

Cylinder tilted:
- Diameter = 8 in → radius r = 8 ÷ 2 = 4 in
- Height h = 12 in

SA = 2 × 3.14 × (4)² + 2 × 3.14 × 4 × 12
= 2 × 3.14 × 16 + 2 × 3.14 × 48
= 6.28 × 16 + 6.28 × 48
= 100.48 + 301.44
= 401.92

Round → 402

✔ Answer 4: 402

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Problem 5:

Upright cylinder:
- Diameter = 6 in → radius r = 6 ÷ 2 = 3 in
- Height h = 3 in

SA = 2 × 3.14 × (3)² + 2 × 3.14 × 3 × 3
= 2 × 3.14 × 9 + 2 × 3.14 × 9
= 6.28 × 9 + 6.28 × 9
= 56.52 + 56.52
= 113.04

Round → 113

✔ Answer 5: 113

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Problem 6:

Cylinder lying on its side:
- Diameter = 10 in → radius r = 10 ÷ 2 = 5 in
- Height h = 2 in

SA = 2 × 3.14 × (5)² + 2 × 3.14 × 5 × 2
= 2 × 3.14 × 25 + 2 × 3.14 × 10
= 6.28 × 25 + 6.28 × 10
= 157 + 62.8
= 219.8

Round → 220

✔ Answer 6: 220

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Final Answer:
1. 151
2. 187
3. 53
4. 402
5. 113
6. 220