Question

terry is filling spherical water balloons with a faucet that puts out 100 cm³ of water per second. at that rate, it takes terry 6 seconds to fill a balloon. what is the radius of a filled balloon? round to the nearest centimeter. cm

Explanation:

Step1: Find the volume of the balloon

The faucet puts out \(100\space cm^3\) per second and it takes 6 seconds to fill the balloon. So the volume \(V\) of the balloon is the rate times time.
\(V = 100\times6 = 600\space cm^3\)

Step2: Use the formula for the volume of a sphere

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^3\), where \(r\) is the radius. We know \(V = 600\), so we can solve for \(r\).
First, rearrange the formula to solve for \(r^3\):
\(r^3=\frac{3V}{4\pi}\)
Substitute \(V = 600\) into the formula:
\(r^3=\frac{3\times600}{4\pi}=\frac{1800}{4\pi}=\frac{450}{\pi}\)

Step3: Calculate the radius

Now, find \(r\) by taking the cube root of \(\frac{450}{\pi}\).
First, calculate \(\frac{450}{\pi}\approx\frac{450}{3.1416}\approx143.24\)
Then, \(r=\sqrt[3]{143.24}\approx5.23\)
Rounding to the nearest centimeter, \(r\approx5\)

Answer:

5