Quick answer: A sphere of radius r has surface area 4πr² and volume (4/3)πr³. Surface area measures its boundary; volume measures the space enclosed.
Worked example
Find surface area and volume of a sphere of radius 3 cm.
- Surface area = 4π×3² = 36π cm².
- Volume = (4/3)π×3³ = (4/3)π×27.
- Volume = 36π cm³.
Check the result
The numerical coefficients happen to match at radius 3, but their units and meanings differ.
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Common mistake to avoid
Do not use diameter as radius. A hemisphere has half the sphere's volume, but its total surface also includes a circular base.
Try it yourself
1. Find surface area for radius 2 cm. 2. Find volume for radius 6 cm.
Answers and reasoning
1. 16π cm². 2. (4/3)π216 = 288π cm³; doubling radius from 3 to 6 multiplies volume by 8.
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