To find the total surface area of a cylinder, we use this formula:
Total Surface Area = 2πr² + 2πrh
Where:
-
r is the radius (half the diameter)
-
h is the height (or length) of the cylinder
-
π = 3.14 (as instructed)
We’ll calculate each one step by step and round to the nearest whole number.
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Problem 1:
Diameter = 8 in → Radius r = 4 in
Height h = 2 in
Surface Area = 2 × 3.14 × 4² + 2 × 3.14 × 4 × 2
= 2 × 3.14 × 16 + 2 × 3.14 × 8
= 100.48 + 50.24
=
150.72 → Round to
151
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Problem 2:
Radius r = 3.5 in
Height h = 5 in
Surface Area = 2 × 3.14 × (3.5)² + 2 × 3.14 × 3.5 × 5
First: 3.5² = 12.25
→ 2 × 3.14 × 12.25 = 76.93
Second: 2 × 3.14 × 3.5 × 5 = 109.9
Total = 76.93 + 109.9 =
186.83 → Round to
187
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Problem 3:
Diameter = 4 in → Radius r = 2 in
Height h = 2.25 in
Surface Area = 2 × 3.14 × 2² + 2 × 3.14 × 2 × 2.25
= 2 × 3.14 × 4 + 2 × 3.14 × 4.5
= 25.12 + 28.26
=
53.38 → Round to
53
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Problem 4:
Diameter = 8 in → Radius r = 4 in
Height h = 12 in
Surface Area = 2 × 3.14 × 4² + 2 × 3.14 × 4 × 12
= 2 × 3.14 × 16 + 2 × 3.14 × 48
= 100.48 + 301.44
=
401.92 → Round to
402
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Problem 5:
Diameter = 6 m → Radius r = 3 m
Height h = 3 m
Surface Area = 2 × 3.14 × 3² + 2 × 3.14 × 3 × 3
= 2 × 3.14 × 9 + 2 × 3.14 × 9
= 56.52 + 56.52
=
113.04 → Round to
113
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Problem 6:
Diameter = 10 in → Radius r = 5 in
Height h = 2 in
Surface Area = 2 × 3.14 × 5² + 2 × 3.14 × 5 × 2
= 2 × 3.14 × 25 + 2 × 3.14 × 10
= 157 + 62.8
=
219.8 → Round to
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 of cylinder worksheet.
