5 the radius of a basketball is 4.7 inches. what is the volume of the basketball? round to the nearest tenth. (example 2) 6. jackie bought a game that contained a ball and 10 jacks. the ball had a radius of 2 inches. what is the volume of the ball? round to the nearest tenth. (example 2) 7. a spherical ball has a diameter of 8 inches. the ball has a slow leak in which the air escapes at the rate of 2.5 cubic inches per second. how long it would take the ball to deflate? round to the nearest tenth. (example 3)

Question

Accepted Answer

# Explanation:
## Step1: Find the volume formula for a sphere
The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$, where $r$ is the radius of the sphere.
## Step2: Calculate the volume for problem 5
Given $r = 4.7$ inches.
$$
\begin{align*}
V&=\frac{4}{3}\times\pi\times(4.7)^{3}\
&=\frac{4}{3}\times\pi\times103.823\
&\approx\frac{4}{3}\times3.14\times103.823\
&=\frac{1291.97704}{3}\
&\approx430.7
\end{align*}
$$
## Step3: Calculate the volume for problem 6
Given $r = 2$ inches.
$$
\begin{align*}
V&=\frac{4}{3}\times\pi\times(2)^{3}\
&=\frac{4}{3}\times\pi\times8\
&\approx\frac{4}{3}\times3.14\times8\
&=\frac{100.48}{3}\
&\approx33.5
\end{align*}
$$
## Step4: Calculate the volume for problem 7
First, find the radius. Given diameter $d = 8$ inches, so $r=\frac{d}{2}=4$ inches.
$$
\begin{align*}
V&=\frac{4}{3}\times\pi\times(4)^{3}\
&=\frac{4}{3}\times\pi\times64\
&\approx\frac{4}{3}\times3.14\times64\
&=\frac{803.84}{3}\
&\approx267.9
\end{align*}
$$
Then, find the time. The rate of air escape is $2.5$ cubic inches per second. Time $t=\frac{V}{rate}$, so $t=\frac{267.9}{2.5}=107.2$ seconds.

# Answer:
5. $430.7$ cubic inches
6. $33.5$ cubic inches
7. $107.2$ seconds

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QUESTION IMAGE

Question

Explanation:

Step1: Find the volume formula for a sphere

Step2: Calculate the volume for problem 5

Step3: Calculate the volume for problem 6

Step4: Calculate the volume for problem 7

Answer: