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. 201.1 ft³ 410.3 ft³ 205.3 ft³ 67.0 ft³

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Accepted Answer

# Explanation:
## Step1: Recall the volume formula for a sphere.
The volume $ V $ of a sphere is given by the formula $ V = \frac{4}{3}\pi r^3 $, where $ r $ is the radius of the sphere.

## Step2: Calculate the volume of the first balloon (radius $ r_1 = 3 $ feet).
Substitute $ r = 3 $ and $ \pi = 3.14 $ into the formula:
$$
\begin{align*}
V_1&=\frac{4}{3}\times3.14\times3^3\
&=\frac{4}{3}\times3.14\times27\
& = 4\times3.14\times9\
& = 113.04 \text{ cubic feet}
\end{align*}
$$

## Step3: Calculate the volume of the second balloon (radius $ r_2 = 5 $ feet).
Substitute $ r = 5 $ and $ \pi = 3.14 $ into the formula:
$$
\begin{align*}
V_2&=\frac{4}{3}\times3.14\times5^3\
&=\frac{4}{3}\times3.14\times125\
&=\frac{4\times3.14\times125}{3}\
&=\frac{1570}{3}\
&\approx523.33 \text{ cubic feet}
\end{align*}
$$

## Step4: Find the difference in volumes.
Subtract the volume of the smaller balloon from the volume of the larger balloon:
$$
\begin{align*}
V_2 - V_1&= 523.33 - 113.04\
& = 410.29\
&\approx410.3 \text{ cubic feet}
\end{align*}
$$

# Answer:
410.3 $ \text{ft}^3 $ (the option with 410.3 $ \text{ft}^3 $)

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Question

Explanation:

Step1: Recall the volume formula for a sphere.

Step2: Calculate the volume of the first balloon (radius \( r_1 = 3 \) feet).

Step3: Calculate the volume of the second balloon (radius \( r_2 = 5 \) feet).

Step4: Find the difference in volumes.

Answer: