To find the surface area of a sphere, we use the formula:
Surface Area = 4 × π × r²
Where:
-
r is the radius of the sphere.
-
π (pi) is approximately
3.1416, but for this worksheet, we’ll use
3.14 unless told otherwise — however, since answers are to 1 decimal place, using more precise π (like 3.14159) will help accuracy. We’ll use
π ≈ 3.1416 and round final answer to 1 decimal.
Also note: If diameter is given, divide by 2 to get radius.
Let’s solve each one step by step.
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Problem 1: Diameter = 2¼ m → Radius = 2.25 ÷ 2 = 1.125 m
Area = 4 × π × (1.125)²
= 4 × 3.1416 × 1.265625
First: 3.1416 × 1.265625 ≈ 3.976
Then: 4 × 3.976 ≈ 15.904
→ Round to 1 decimal:
15.9 m²
Wait — let me recalculate with more precision:
(1.125)² = 1.265625
4 × π × 1.265625 = 4 × 3.1415926535 × 1.265625
≈ 4 × 3.976078... ≈ 15.9043 →
15.9 m²
✔ Correct.
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Problem 2: Diameter = 7 cm → Radius = 3.5 cm
Area = 4 × π × (3.5)²
= 4 × π × 12.25
= 49 × π
≈ 49 × 3.1415926535 ≈ 153.938
→ Round to 1 decimal:
153.9 cm²
✔ Correct.
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Problem 3: Diameter = 3½ in → Radius = 3.5 ÷ 2 = 1.75 in
Area = 4 × π × (1.75)²
= 4 × π × 3.0625
= 12.25 × π
≈ 12.25 × 3.1415926535 ≈ 38.4845
→ Round to 1 decimal:
38.5 in²
✔ Correct.
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Problem 4: Radius = 17 in (given directly)
Area = 4 × π × (17)²
= 4 × π × 289
= 1156 × π
≈ 1156 × 3.1415926535 ≈ 3631.681
→ Round to 1 decimal:
3631.7 in²
✔ Correct.
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Problem 5: Diameter = 15.3 cm → Radius = 15.3 ÷ 2 = 7.65 cm
Area = 4 × π × (7.65)²
First: 7.65² = 58.5225
Then: 4 × π × 58.5225 = 234.09 × π
≈ 234.09 × 3.1415926535 ≈ 735.416
→ Round to 1 decimal:
735.4 cm²
Let me double-check:
7.65 × 7.65 = (7 + 0.65)² = 49 + 2×7×0.65 + 0.65² = 49 + 9.1 + 0.4225 = 58.5225 ✔️
4 × 58.5225 = 234.09 ✔️
234.09 × 3.1415926535:
Break it down:
234 × 3.1415926535 ≈ 735.132
0.09 × 3.1415926535 ≈ 0.2827
Total ≈ 735.4147 → rounds to
735.4 cm²
✔ Correct.
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Final Answer:
1) 15.9 m²
2) 153.9 cm²
3) 38.5 in²
4) 3631.7 in²
5) 735.4 cm²
Parent Tip: Review the logic above to help your child master the concept of surface area of spheres worksheet.
