Math worksheet for calculating the surface area and volume of spheres, featuring nine problems with varying radii.

Let’s solve each problem step by step. We’ll use the formulas for surface area and volume of a sphere:

- Surface Area (SA) = 4πr²
- Volume (V) = (4/3)πr³

We’ll round answers to the nearest hundredth if needed, as instructed.

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Problem 1: Radius = 11 ft

SA = 4 × π × (11)² = 4 × π × 121 = 484π ≈ 484 × 3.1416 ≈ 1520.53 ft²
V = (4/3) × π × (11)³ = (4/3) × π × 1331 = (5324/3)π ≈ 1774.6667 × 3.1416 ≈ 5575.28 ft³

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Problem 2: Radius = 6 in

SA = 4 × π × 36 = 144π ≈ 144 × 3.1416 ≈ 452.39 in²
V = (4/3) × π × 216 = 288π ≈ 288 × 3.1416 ≈ 904.78 in³

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Problem 3: Radius = 13 in

SA = 4 × π × 169 = 676π ≈ 676 × 3.1416 ≈ 2123.72 in²
V = (4/3) × π × 2197 = (8788/3)π ≈ 2929.333 × 3.1416 ≈ 9202.77 in³

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Problem 4: Radius = 2 cm

SA = 4 × π × 4 = 16π ≈ 16 × 3.1416 ≈ 50.27 cm²
V = (4/3) × π × 8 = (32/3)π ≈ 10.6667 × 3.1416 ≈ 33.51 cm³

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Problem 5: Radius = 5 mm

SA = 4 × π × 25 = 100π ≈ 100 × 3.1416 ≈ 314.16 mm²
V = (4/3) × π × 125 = (500/3)π ≈ 166.6667 × 3.1416 ≈ 523.60 mm³

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Problem 6: Radius = 8 mm

SA = 4 × π × 64 = 256π ≈ 256 × 3.1416 ≈ 804.25 mm²
V = (4/3) × π × 512 = (2048/3)π ≈ 682.6667 × 3.1416 ≈ 2144.66 mm³

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Problem 7: Radius = 2 ft

Same as Problem 4 but in feet.

SA = 4 × π × 4 = 16π ≈ 50.27 ft²
V = (4/3) × π × 8 = (32/3)π ≈ 33.51 ft³

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Problem 8: Radius = 14 yd

SA = 4 × π × 196 = 784π ≈ 784 × 3.1416 ≈ 2463.01 yd²
V = (4/3) × π × 2744 = (10976/3)π ≈ 3658.6667 × 3.1416 ≈ 11494.04 yd³

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Problem 9: Radius = 9 cm

SA = 4 × π × 81 = 324π ≈ 324 × 3.1416 ≈ 1017.88 cm²
V = (4/3) × π × 729 = 972π ≈ 972 × 3.1416 ≈ 3053.63 cm³

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Final Answer:

1) Surface Area: 1520.53 ft², Volume: 5575.28 ft³
2) Surface Area: 452.39 in², Volume: 904.78 in³
3) Surface Area: 2123.72 in², Volume: 9202.77 in³
4) Surface Area: 50.27 cm², Volume: 33.51 cm³
5) Surface Area: 314.16 mm², Volume: 523.60 mm³
6) Surface Area: 804.25 mm², Volume: 2144.66 mm³
7) Surface Area: 50.27 ft², Volume: 33.51 ft³
8) Surface Area: 2463.01 yd², Volume: 11494.04 yd³
9) Surface Area: 1017.88 cm², Volume: 3053.63 cm³