Question

1. sarah is blowing up spherical balloons for her brothers birthday party. one of the balloons has a radius of 3 inches. round to the nearest tenth. (examples 2 and 3) a. what is the volume of the balloon? b. suppose sarah can inflate the balloon at a rate of 200 cubic inches per minute. how long will it take her to inflate the ballon?

Explanation:

Step1: Calculate the volume of the spherical balloon

The formula for the volume of a sphere is \(V = \frac{4}{3}\pi r^{3}\). Given \(r = 3\) inches.
Substitute \(r = 3\) into the formula:
\(V=\frac{4}{3}\pi(3)^{3}=\frac{4}{3}\pi\times27 = 36\pi\)
Using \(\pi\approx3.14\), \(V = 36\times3.14=113.04\approx113.0\) cubic inches.

Step2: Calculate the time to inflate the balloon

We know the rate of inflation is \(200\) cubic inches per minute. Let \(t\) be the time.
Using the formula \(t=\frac{V}{rate}\), with \(V = 113.0\) (from part a) and rate \(= 200\)
\(t=\frac{113.0}{200}=0.565\approx0.6\) minutes

Answer:

a. \(113.0\) cubic inches
b. \(0.6\) minutes