Let’s solve each problem step by step. We’re finding the
total surface area of each cylinder.
The formula for total surface area of a cylinder is:
>
Surface Area = 2πr² + 2πrh
Where:
- r = radius (half of the diameter)
- h = height (or length, depending on how the cylinder is drawn)
- π = 3.14 (as instructed)
We’ll calculate each one carefully and round to the nearest whole number at the end.
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Problem 1:
Diameter = 8 in → Radius = 4 in
Height = 2 in
SA = 2 × 3.14 × (4)² + 2 × 3.14 × 4 × 2
= 2 × 3.14 × 16 + 2 × 3.14 × 8
= 100.48 + 50.24
=
150.72 → Round to 151
✔ Answer:
151
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Problem 2:
This cylinder is lying on its side. The circular face has radius 3.5 in, and the length (height) is 5 in.
So: r = 3.5, h = 5
SA = 2 × 3.14 × (3.5)² + 2 × 3.14 × 3.5 × 5
First, 3.5² = 12.25
→ 2 × 3.14 × 12.25 = 76.93
→ 2 × 3.14 × 3.5 × 5 = 109.9
Total = 76.93 + 109.9 =
186.83 → Round to 187
✔ Answer:
187
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Problem 3:
Diameter = 4 ft → Radius = 2 ft
Length (height) = 2.25 ft
SA = 2 × 3.14 × (2)² + 2 × 3.14 × 2 × 2.25
= 2 × 3.14 × 4 + 2 × 3.14 × 4.5
= 25.12 + 28.26
=
53.38 → Round to 53
✔ Answer:
53
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Problem 4:
Diameter = 8 in → Radius = 4 in
Length (height) = 12 in
SA = 2 × 3.14 × (4)² + 2 × 3.14 × 4 × 12
= 2 × 3.14 × 16 + 2 × 3.14 × 48
= 100.48 + 301.44
=
401.92 → Round to 402
✔ Answer:
402
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Problem 5:
Diameter = 6 m → Radius = 3 m
Height = 3 m
SA = 2 × 3.14 × (3)² + 2 × 3.14 × 3 × 3
= 2 × 3.14 × 9 + 2 × 3.14 × 9
= 56.52 + 56.52
=
113.04 → Round to 113
✔ Answer:
113
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Problem 6:
Diameter = 10 ft → Radius = 5 ft
Length (height) = 2 ft
SA = 2 × 3.14 × (5)² + 2 × 3.14 × 5 × 2
= 2 × 3.14 × 25 + 2 × 3.14 × 10
= 157 + 62.8
=
219.8 → Round to 220
✔ Answer:
220
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Final Answer:
1. 151
2. 187
3. 53
4. 402
5. 113
6. 220
Parent Tip: Review the logic above to help your child master the concept of surface area and volume of cylinders worksheet.
