Let’s solve each problem step by step. We’ll use the correct formulas for surface area of cylinders and cones.
---
Formulas to remember:
Cylinder Surface Area (including top and bottom):
SA = 2πr² + 2πrh
= 2πr(r + h)
🔹
Cone Surface Area (including base):
SA = πr² + πrl
= πr(r + l)
where *l* is the slant height (the side length, not the vertical height).
️ Note: In some problems, they give you the slant height directly (like in #2, #4, #5, #8, #9). In others, if only radius and vertical height are given, we’d need to use Pythagoras to find slant height — but looking at the diagrams, all cone problems here already give the slant height (the diagonal side), so we can use it directly.
Also, round answers to nearest hundredth (two decimal places) when needed.
We’ll use π ≈ 3.1416 for calculations.
---
Problem 1: Cylinder
Radius r = 8 ft, Height h = 12 ft
SA = 2πr(r + h)
= 2 × π × 8 × (8 + 12)
= 2 × π × 8 × 20
= 320π
≈ 320 × 3.1416 =
1005.31 ft²
✔ Final Answer for #1:
1005.31
---
Problem 2: Cone
Radius r = 4 in, Slant height l = 6 in
SA = πr(r + l)
= π × 4 × (4 + 6)
= π × 4 × 10
= 40π
≈ 40 × 3.1416 =
125.66 in²
✔ Final Answer for #2:
125.66
---
Problem 3: Cylinder
Radius r = 6 yd, Height h = 8 yd
SA = 2πr(r + h)
= 2 × π × 6 × (6 + 8)
= 2 × π × 6 × 14
= 168π
≈ 168 × 3.1416 =
527.79 yd²
✔ Final Answer for #3:
527.79
---
Problem 4: Cone
Radius r = 5 mm, Slant height l = 13 mm
SA = πr(r + l)
= π × 5 × (5 + 13)
= π × 5 × 18
= 90π
≈ 90 × 3.1416 =
282.74 mm²
✔ Final Answer for #4:
282.74
---
Problem 5: Cone
Radius r = 6 mm, Slant height l = 14 mm
SA = πr(r + l)
= π × 6 × (6 + 14)
= π × 6 × 20
= 120π
≈ 120 × 3.1416 =
376.99 mm²
✔ Final Answer for #5:
376.99
---
Problem 6: Cylinder
Radius r = 6 cm, Height h = 8 cm
SA = 2πr(r + h)
= 2 × π × 6 × (6 + 8)
= 2 × π × 6 × 14
= 168π
≈ 168 × 3.1416 =
527.79 cm²
✔ Final Answer for #6:
527.79
---
Problem 7: Cylinder
Radius r = 7 yd, Height h = 10 yd
SA = 2πr(r + h)
= 2 × π × 7 × (7 + 10)
= 2 × π × 7 × 17
= 238π
≈ 238 × 3.1416 =
747.70 yd²
✔ Final Answer for #7:
747.70
---
Problem 8: Cone
Radius r = 7 ft, Slant height l = 10 ft
SA = πr(r + l)
= π × 7 × (7 + 10)
= π × 7 × 17
= 119π
≈ 119 × 3.1416 =
373.85 ft²
✔ Final Answer for #8:
373.85
---
Problem 9: Cone
Radius r = 4 cm, Slant height l = 6 cm
SA = πr(r + l)
= π × 4 × (4 + 6)
= π × 4 × 10
= 40π
≈ 40 × 3.1416 =
125.66 cm²
✔ Final Answer for #9:
125.66
---
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 area and volume practice.
