Surface Area of Cones Worksheets - Free Printable
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Step-by-step solution for: Surface Area of Cones Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Surface Area of Cones Worksheets
Let’s solve each cone’s surface area step by step.
We’re told to use π = 3.14 and round answers to two decimal places.
The formula for the surface area of a cone is:
> Surface Area = πr² + πrl
> where:
> - r = radius of the base
> - l = slant height (the diagonal side from tip to edge of base)
Sometimes we’re given the vertical height (h), not the slant height (l). In that case, we must first find the slant height using the Pythagorean theorem:
> l = √(r² + h²)
---
Given: radius = 7 in, slant height = 20 in
SA = πr² + πrl
= 3.14 × 7² + 3.14 × 7 × 20
= 3.14 × 49 + 3.14 × 140
= 153.86 + 439.6
= 593.46 in²
---
Given: radius = 10 ft, vertical height = 22 ft → need slant height
l = √(10² + 22²) = √(100 + 484) = √584 ≈ 24.166
SA = πr² + πrl
= 3.14 × 100 + 3.14 × 10 × 24.166
= 314 + 3.14 × 241.66
= 314 + 758.8124
≈ 1072.81 ft²
*(Check: 3.14 × 241.66 = let's compute: 241.66 × 3 = 724.98, 241.66 × 0.14 = 33.8324 → total 758.8124 — correct)*
---
Given: radius = 2 m, slant height = 10 m
SA = πr² + πrl
= 3.14 × 4 + 3.14 × 2 × 10
= 12.56 + 62.8
= 75.36 m²
---
Given: radius = 9 cm, slant height = 15 cm
SA = πr² + πrl
= 3.14 × 81 + 3.14 × 9 × 15
= 254.34 + 3.14 × 135
= 254.34 + 423.9
= 678.24 cm²
---
Given: radius = 6 in, vertical height = 11 in → find slant height
l = √(6² + 11²) = √(36 + 121) = √157 ≈ 12.53
SA = πr² + πrl
= 3.14 × 36 + 3.14 × 6 × 12.53
= 113.04 + 3.14 × 75.18
= 113.04 + 236.0652
≈ 349.11 in²
*(Check: 75.18 × 3.14 → 75×3.14=235.5, 0.18×3.14≈0.5652 → total 236.0652 — correct)*
---
Given: radius = 11 yd, slant height = 18 yd
SA = πr² + πrl
= 3.14 × 121 + 3.14 × 11 × 18
= 379.94 + 3.14 × 198
= 379.94 + 621.72
= 1001.66 yd²
---
Given: radius = 4 m, vertical height = 12 m → find slant height
l = √(4² + 12²) = √(16 + 144) = √160 ≈ 12.649
SA = πr² + πrl
= 3.14 × 16 + 3.14 × 4 × 12.649
= 50.24 + 3.14 × 50.596
= 50.24 + 158.87144
≈ 209.11 m²
*(Check: 50.596 × 3.14 → 50×3.14=157, 0.596×3.14≈1.871 → total ~158.871 — correct)*
---
Given: radius = 12 cm, slant height = 16 cm
SA = πr² + πrl
= 3.14 × 144 + 3.14 × 12 × 16
= 452.16 + 3.14 × 192
= 452.16 + 602.88
= 1055.04 cm²
---
Given: radius = 5 in, vertical height = 14 in → find slant height
l = √(5² + 14²) = √(25 + 196) = √221 ≈ 14.866
SA = πr² + πrl
= 3.14 × 25 + 3.14 × 5 × 14.866
= 78.5 + 3.14 × 74.33
= 78.5 + 233.3962
≈ 311.90 in²
*(Check: 74.33 × 3.14 → 74×3.14=232.36, 0.33×3.14≈1.0362 → total 233.3962 — correct)*
---
Final Answer:
1) 593.46 in²
2) 1072.81 ft²
3) 75.36 m²
4) 678.24 cm²
5) 349.11 in²
6) 1001.66 yd²
7) 209.11 m²
8) 1055.04 cm²
9) 311.90 in²
We’re told to use π = 3.14 and round answers to two decimal places.
The formula for the surface area of a cone is:
> Surface Area = πr² + πrl
> where:
> - r = radius of the base
> - l = slant height (the diagonal side from tip to edge of base)
Sometimes we’re given the vertical height (h), not the slant height (l). In that case, we must first find the slant height using the Pythagorean theorem:
> l = √(r² + h²)
---
Problem 1:
Given: radius = 7 in, slant height = 20 in
SA = πr² + πrl
= 3.14 × 7² + 3.14 × 7 × 20
= 3.14 × 49 + 3.14 × 140
= 153.86 + 439.6
= 593.46 in²
---
Problem 2:
Given: radius = 10 ft, vertical height = 22 ft → need slant height
l = √(10² + 22²) = √(100 + 484) = √584 ≈ 24.166
SA = πr² + πrl
= 3.14 × 100 + 3.14 × 10 × 24.166
= 314 + 3.14 × 241.66
= 314 + 758.8124
≈ 1072.81 ft²
*(Check: 3.14 × 241.66 = let's compute: 241.66 × 3 = 724.98, 241.66 × 0.14 = 33.8324 → total 758.8124 — correct)*
---
Problem 3:
Given: radius = 2 m, slant height = 10 m
SA = πr² + πrl
= 3.14 × 4 + 3.14 × 2 × 10
= 12.56 + 62.8
= 75.36 m²
---
Problem 4:
Given: radius = 9 cm, slant height = 15 cm
SA = πr² + πrl
= 3.14 × 81 + 3.14 × 9 × 15
= 254.34 + 3.14 × 135
= 254.34 + 423.9
= 678.24 cm²
---
Problem 5:
Given: radius = 6 in, vertical height = 11 in → find slant height
l = √(6² + 11²) = √(36 + 121) = √157 ≈ 12.53
SA = πr² + πrl
= 3.14 × 36 + 3.14 × 6 × 12.53
= 113.04 + 3.14 × 75.18
= 113.04 + 236.0652
≈ 349.11 in²
*(Check: 75.18 × 3.14 → 75×3.14=235.5, 0.18×3.14≈0.5652 → total 236.0652 — correct)*
---
Problem 6:
Given: radius = 11 yd, slant height = 18 yd
SA = πr² + πrl
= 3.14 × 121 + 3.14 × 11 × 18
= 379.94 + 3.14 × 198
= 379.94 + 621.72
= 1001.66 yd²
---
Problem 7:
Given: radius = 4 m, vertical height = 12 m → find slant height
l = √(4² + 12²) = √(16 + 144) = √160 ≈ 12.649
SA = πr² + πrl
= 3.14 × 16 + 3.14 × 4 × 12.649
= 50.24 + 3.14 × 50.596
= 50.24 + 158.87144
≈ 209.11 m²
*(Check: 50.596 × 3.14 → 50×3.14=157, 0.596×3.14≈1.871 → total ~158.871 — correct)*
---
Problem 8:
Given: radius = 12 cm, slant height = 16 cm
SA = πr² + πrl
= 3.14 × 144 + 3.14 × 12 × 16
= 452.16 + 3.14 × 192
= 452.16 + 602.88
= 1055.04 cm²
---
Problem 9:
Given: radius = 5 in, vertical height = 14 in → find slant height
l = √(5² + 14²) = √(25 + 196) = √221 ≈ 14.866
SA = πr² + πrl
= 3.14 × 25 + 3.14 × 5 × 14.866
= 78.5 + 3.14 × 74.33
= 78.5 + 233.3962
≈ 311.90 in²
*(Check: 74.33 × 3.14 → 74×3.14=232.36, 0.33×3.14≈1.0362 → total 233.3962 — correct)*
---
Final Answer:
1) 593.46 in²
2) 1072.81 ft²
3) 75.36 m²
4) 678.24 cm²
5) 349.11 in²
6) 1001.66 yd²
7) 209.11 m²
8) 1055.04 cm²
9) 311.90 in²
Parent Tip: Review the logic above to help your child master the concept of surface area of a cone worksheet.
