A spherical balloon is filled with 4500p 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`

Explanation

`V_i = 4500 pi m^3`

`(d V_i)/(dt) = -72 pi m^3/(min)`

`V_(49 min) = 4500 pi - (72 pi xx 49) = 4500 pi - 3528 pi`

`= 972 pi m^3 `

`V= 4/3 pi r^3`

at 49 min,`972 = 4/3 xx pi xx r^3`

`r^3 = 3 xx 972/4`

`r= 3^2 = 9 m`

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