Let’s solve each problem one by one. We’ll use the correct formulas for surface area of cylinders and cones.
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For Cylinders:
Surface Area = 2πr² + 2πrh
= 2πr(r + h)
Where:
- r = radius
- h = height
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For Cones:
Surface Area = πr² + πrl
= πr(r + l)
Where:
- r = radius
- l = slant height (the diagonal side, NOT the vertical height)
Note: In some problems, you’re given the vertical height — but for cone surface area, we need the
slant height. If only vertical height is given, we must use Pythagoras to find slant height:
l = √(r² + h²)
But in this worksheet, all cone problems give the
slant height directly (marked with an arrow along the side), so we don’t need to calculate it.
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We’ll use π ≈ 3.1416 and round answers to nearest hundredth as instructed.
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Problem 1: Cylinder
Radius = 8 ft, Height = 12 ft
SA = 2πr(r + h) = 2 × π × 8 × (8 + 12) = 16π × 20 = 320π
320 × 3.1416 ≈ 1005.31 ft²
✔ Answer: 1005.31
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Problem 2: Cone
Radius = 4 in, Slant height = 6 in
SA = πr(r + l) = π × 4 × (4 + 6) = 4π × 10 = 40π
40 × 3.1416 ≈ 125.66 in²
✔ Answer: 125.66
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Problem 3: Cylinder
Radius = 6 yd, Height = 8 yd
SA = 2πr(r + h) = 2 × π × 6 × (6 + 8) = 12π × 14 = 168π
168 × 3.1416 ≈ 527.79 yd²
✔ Answer: 527.79
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Problem 4: Cone
Radius = 5 mm, Slant height = 13 mm
SA = πr(r + l) = π × 5 × (5 + 13) = 5π × 18 = 90π
90 × 3.1416 ≈ 282.74 mm²
✔ Answer: 282.74
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Problem 5: Cone
Radius = 6 mm, Slant height = 14 mm
SA = πr(r + l) = π × 6 × (6 + 14) = 6π × 20 = 120π
120 × 3.1416 ≈ 376.99 mm²
✔ Answer: 376.99
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Problem 6: Cylinder
Radius = 6 cm, Height = 8 cm
SA = 2πr(r + h) = 2 × π × 6 × (6 + 8) = 12π × 14 = 168π
168 × 3.1416 ≈ 527.79 cm²
✔ Answer: 527.79
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Problem 7: Cylinder
Radius = 7 yd, Height = 10 yd
SA = 2πr(r + h) = 2 × π × 7 × (7 + 10) = 14π × 17 = 238π
238 × 3.1416 ≈ 747.70 yd²
✔ Answer: 747.70
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Problem 8: Cone
Radius = 7 ft, Slant height = 10 ft
SA = πr(r + l) = π × 7 × (7 + 10) = 7π × 17 = 119π
119 × 3.1416 ≈ 373.85 ft²
✔ Answer: 373.85
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Problem 9: Cone
Radius = 4 cm, Slant height = 6 cm
SA = πr(r + l) = π × 4 × (4 + 6) = 4π × 10 = 40π
40 × 3.1416 ≈ 125.66 cm²
✔ Answer: 125.66
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Final Answer:
1) 1005.31
2) 125.66
3) 527.79
4) 282.74
5) 376.99
6) 527.79
7) 747.70
8) 373.85
9) 125.66
Parent Tip: Review the logic above to help your child master the concept of volume of spheres cones and cylinders worksheet.
