Let's solve this step-by-step to find the radius of the soccer ball.
### Step 1: Given Information
We are given that the volume [tex]\( V \)[/tex] of the soccer ball is [tex]\( 371 \)[/tex] cubic inches, and we are asked to use [tex]\( \pi = 3.14 \)[/tex]. We need to find the radius [tex]\( r \)[/tex].
### Step 2: Formula for the Volume of a Sphere
The formula for the volume of a sphere is:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
### Step 3: Plug in the Given Values
Substitute [tex]\( V = 371 \)[/tex] and [tex]\( \pi = 3.14 \)[/tex] into the formula:
[tex]\[ 371 = \frac{4}{3} \times 3.14 \times r^3 \][/tex]
### Step 4: Solve for [tex]\( r^3 \)[/tex]
First, simplify the right-hand side of the equation:
[tex]\[ \frac{4}{3} \times 3.14 = 4.18666667 \][/tex]
So we have:
[tex]\[ 371 = 4.18666667 \times r^3 \][/tex]
Next, isolate [tex]\( r^3 \)[/tex] by dividing both sides by 4.18666667:
[tex]\[ r^3 = \frac{371}{4.18666667} \][/tex]
[tex]\[ r^3 \approx 88.61465 \][/tex]
### Step 5: Take the Cube Root to Find [tex]\( r \)[/tex]
To find [tex]\( r \)[/tex], we take the cube root of [tex]\( r^3 \)[/tex]:
[tex]\[ r \approx \sqrt[3]{88.61465} \][/tex]
[tex]\[ r \approx 4.45829 \][/tex]
### Step 6: Round to the Nearest Tenth
Finally, we round this value to the nearest tenth:
[tex]\[ r \approx 4.5 \][/tex]
### Conclusion
The radius of the soccer ball, to the nearest tenth of an inch, is approximately [tex]\( 4.5 \)[/tex] inches.
Thus, the answer is:
B. 4.5 inches
