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A spherical balloon is filled with 4500p...

A spherical balloon is filled with 4500pie cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of `72pi` cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is (1) `9/7` (2) `7/9` (3) `2/9` (4) `9/2`

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To solve the problem step by step, we will follow these steps: ### Step 1: Understand the problem We need to find the rate at which the radius of a spherical balloon decreases after a certain time, given the volume of the balloon and the rate at which gas is escaping. ### Step 2: Write down the volume formula for a sphere The volume \( V \) of a sphere is given by the formula: \[ ...
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