Question

adair advertising has 2 spherical balloons. one has a radius of 3 feet and the other one has a radius of 5 feet. what is the difference in the volume of the two balloons, rounded to the nearest tenth of a cubic foot? use 3.14 for π. 67.0 ft³ 205.3 ft³ 201.1 ft³ 410.3 ft³

Explanation:

Step1: Calculate the volume of the first balloon

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\). For the balloon with \(r = 3\) feet and \(\pi=3.14\), we have \(V_1=\frac{4}{3}\times3.14\times3^{3}\).
First, calculate \(3^{3}=27\). Then \(V_1=\frac{4}{3}\times3.14\times27\). \(\frac{4}{3}\times27 = 36\), so \(V_1=36\times3.14=113.04\) \(ft^{3}\).

Step2: Calculate the volume of the second balloon

For the balloon with \(r = 5\) feet and \(\pi = 3.14\), using the formula \(V=\frac{4}{3}\pi r^{3}\), we have \(V_2=\frac{4}{3}\times3.14\times5^{3}\).
Calculate \(5^{3}=125\). Then \(V_2=\frac{4}{3}\times3.14\times125\). \(\frac{4\times3.14\times125}{3}=\frac{1570}{3}\approx523.33\) \(ft^{3}\).

Step3: Find the difference in volumes

\(V = V_2 - V_1\). So \(V=523.33-113.04 = 410.29\approx410.3\) \(ft^{3}\).

Answer:

\(410.3\ ft^{3}\)