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.

Explanation:

Step1: Recall the volume formula for a sphere

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$.

Step2: Calculate the volume of the first balloon

For the balloon with $r_1 = 3$ feet, $V_1=\frac{4}{3}\times3.14\times3^{3}=\frac{4}{3}\times3.14\times27 = 4\times3.14\times9=113.04$ cubic - feet.

Step3: Calculate the volume of the second balloon

For the balloon with $r_2 = 5$ feet, $V_2=\frac{4}{3}\times3.14\times5^{3}=\frac{4}{3}\times3.14\times125=\frac{4\times3.14\times125}{3}\approx523.33$ cubic - feet.

Step4: Find the difference in volumes

$V_2 - V_1=523.33 - 113.04 = 410.29\approx410.3$ cubic - feet.

Answer:

$410.3$ ft³