Question
A spherical balloon has a radius of 7 meters. If the
balloon is inflated and the volume increases by 4 times, what will be the new radius of the balloon?Solution
The volume of a sphere is given by V = (4/3)πr³. Let the initial radius be r = 7 meters. Initial volume = (4/3)π(7)³ = (4/3)π(343) = 457.33π m³. If the volume increases by 4 times, the new volume is 4 × 457.33π = 1829.33π m³. Let the new radius be R. Then, (4/3)πR³ = 4 × (4/3)π(7)³, R³ = 4 × 7³, R³ = 4 × 343 = 1372, R ≈ ∛1372 ≈ 11 meters.
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