Question

use the information to answer the question. a spherical 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. minutes

Explanation:

Step1: Calculate balloon volume

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$. With $r = 6$, $V=\frac{4}{3}\pi(6)^{3}=288\pi$ cubic - feet.

Step2: Calculate remaining air volume

Since 20% is lost, 80% remains. So remaining volume is $0.8\times288\pi = 230.4\pi$ cubic - feet.

Step3: Calculate time

Time $t=\frac{230.4\pi}{30}\approx24$ minutes.

Answer:

24