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Aspherical balloon has a radius of 6 feet. Air is leaking out of the balloon at a rate of 30 cubic feet per minute, and the balloon has already lost 20%
of its air
To the nearest minute, how long will it take for the balloon to become completely empty? Enter the answer in the box

Answer 1

Using the volume of the spherical balloon, it is found that it will take 24 hours for the balloon to become completely empty.

What is the volume of a sphere?

The volume of a sphere of radius r is given by:

$V = \frac{4\pi r^3}{3}$

Aspherical balloon has a radius of 6 feet, hence the volume is:

$V = \frac{4\pi 6^3}{3} = 905$

It has already lost 20% of it's air, and air is leaking out of the balloon at a rate of 30 cubic feet per minute, hence the volume after t minutes is given by:

$V(t) = 0.8(905) - 30t$

$V(t) = 724 - 30t$

It will be completely empty when:

$V(t) = 0$

$724 - 30t = 0$

$30t = 724$

$t = \frac{724}{30}$

$t = 24.1$

Rounding, it will take 24 hours for the balloon to become completely empty.

More can be learned about the volume of a sphere at https://brainly.com/question/25608353