Surface area calculation worksheet for cylinders with varying dimensions and units.

Let’s solve each cylinder’s surface area step by step.

The formula for the surface area (SA) of a cylinder is:

SA = 2πr² + 2πrh

Where:
- r = radius
- h = height
- π = 3.14 (as instructed)

We’ll calculate each one carefully, rounding to the nearest tenth at the end.

---

Cylinder 1: radius = 20 cm, height = 42 cm

SA = 2 × 3.14 × (20)² + 2 × 3.14 × 20 × 42
= 2 × 3.14 × 400 + 2 × 3.14 × 840
= 6.28 × 400 + 6.28 × 840
= 2512 + 5275.2
= 7787.2 cm²

---

Cylinder 2: radius = 9 m, height = 7 m

SA = 2 × 3.14 × (9)² + 2 × 3.14 × 9 × 7
= 2 × 3.14 × 81 + 2 × 3.14 × 63
= 6.28 × 81 + 6.28 × 63
= 508.68 + 395.64
= 904.3 m²

---

Cylinder 3: radius = 21 mm, height = 76 mm

SA = 2 × 3.14 × (21)² + 2 × 3.14 × 21 × 76
= 2 × 3.14 × 441 + 2 × 3.14 × 1596
= 6.28 × 441 + 6.28 × 1596
= 2769.48 + 10022.88
= 12792.4 mm²

---

Cylinder 4: radius = 2 m, height = 2 m

SA = 2 × 3.14 × (2)² + 2 × 3.14 × 2 × 2
= 2 × 3.14 × 4 + 2 × 3.14 × 4
= 6.28 × 4 + 6.28 × 4
= 25.12 + 25.12
= 50.2 m²

---

Cylinder 5: radius = 11 cm, height = 17 cm

SA = 2 × 3.14 × (11)² + 2 × 3.14 × 11 × 17
= 2 × 3.14 × 121 + 2 × 3.14 × 187
= 6.28 × 121 + 6.28 × 187
= 759.88 + 1174.36
= 1934.2 cm²

---

Cylinder 6: radius = 3 cm, height = 4 cm

SA = 2 × 3.14 × (3)² + 2 × 3.14 × 3 × 4
= 2 × 3.14 × 9 + 2 × 3.14 × 12
= 6.28 × 9 + 6.28 × 12
= 56.52 + 75.36
= 131.9 cm²

---

Cylinder 7: radius = 42 cm, height = 20 cm

SA = 2 × 3.14 × (42)² + 2 × 3.14 × 42 × 20
= 2 × 3.14 × 1764 + 2 × 3.14 × 840
= 6.28 × 1764 + 6.28 × 840
= 11077.92 + 5275.2
= 16353.1 cm²

---

Cylinder 8: radius = 0.18 m, height = 0.6 m

SA = 2 × 3.14 × (0.18)² + 2 × 3.14 × 0.18 × 0.6
= 2 × 3.14 × 0.0324 + 2 × 3.14 × 0.108
= 6.28 × 0.0324 + 6.28 × 0.108
= 0.203472 + 0.67824
= 0.881712 → rounded to 0.9 m²

Wait — let me double-check that calculation.

0.18² = 0.0324
2 × 3.14 × 0.0324 = 6.28 × 0.0324 = let's compute:

6.28 × 0.03 = 0.1884
6.28 × 0.0024 = 0.015072
Total = 0.203472 ✔️

Now lateral part: 2 × 3.14 × 0.18 × 0.6 = 6.28 × 0.108

6.28 × 0.1 = 0.628
6.28 × 0.008 = 0.05024
Total = 0.67824 ✔️

Sum: 0.203472 + 0.67824 = 0.881712 → rounds to 0.9 m²

But wait — 0.881712 rounded to nearest tenth is 0.9? Yes, because hundredths digit is 8 ≥ 5.

Actually, 0.881712 → tenths place is 8, hundredths is 8 → so yes, round up → 0.9

BUT — let me check if I should keep more precision or if I made an error.

Alternatively, maybe it’s better to write as:

SA = 2πr(r + h) = 2 × 3.14 × 0.18 × (0.18 + 0.6) = 6.28 × 0.18 × 0.78

First: 0.18 × 0.78 = 0.1404
Then: 6.28 × 0.1404 = ?

6 × 0.1404 = 0.8424
0.28 × 0.1404 ≈ 0.039312
Total ≈ 0.881712 → same as before → 0.9 m²

Okay, correct.

---

Cylinder 9: radius = 26 mm, height = 32 mm

SA = 2 × 3.14 × (26)² + 2 × 3.14 × 26 × 32
= 2 × 3.14 × 676 + 2 × 3.14 × 832
= 6.28 × 676 + 6.28 × 832
Compute each:

6.28 × 676:
6 × 676 = 4056
0.28 × 676 = 189.28
Total = 4245.28

6.28 × 832:
6 × 832 = 4992
0.28 × 832 = 232.96
Total = 5224.96

Sum: 4245.28 + 5224.96 = 9470.2 mm²

Wait — let me verify with direct multiplication:

6.28 × 676:

Breakdown:
676 × 6 = 4056
676 × 0.28 = 676 × 0.2 = 135.2; 676 × 0.08 = 54.08 → total 189.28
So 4056 + 189.28 = 4245.28 ✔️

6.28 × 832:

832 × 6 = 4992
832 × 0.28 = 832 × 0.2 = 166.4; 832 × 0.08 = 66.56 → total 232.96
4992 + 232.96 = 5224.96 ✔️

Sum: 4245.28 + 5224.96 = 9470.24 → rounds to 9470.2 mm²

Yes.

---

Final Answers:

Cylinder 1: 7787.2 cm²
Cylinder 2: 904.3 m²
Cylinder 3: 12792.4 mm²
Cylinder 4: 50.2 m²
Cylinder 5: 1934.2 cm²
Cylinder 6: 131.9 cm²
Cylinder 7: 16353.1 cm²
Cylinder 8: 0.9 m²
Cylinder 9: 9470.2 mm²

──────────────────────────────────────

Final Answer:
7787.2, 904.3, 12792.4, 50.2, 1934.2, 131.9, 16353.1, 0.9, 9470.2