To solve for the radius [tex]\( r \)[/tex] in the formula for the volume of a cylinder [tex]\( V = \pi r^2 h \)[/tex], we need to manipulate the formula appropriately.
Given:
- Volume [tex]\( V = 314 \)[/tex] cubic inches
- Height [tex]\( h = 4 \)[/tex] inches
- [tex]\( \pi = 3.14 \)[/tex]
Let's start with the formula:
[tex]\[ V = \pi r^2 h \][/tex]
We need to solve for [tex]\( r \)[/tex]. First, isolate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = \frac{V}{\pi h} \][/tex]
Substitute in the given values:
[tex]\[ r^2 = \frac{314}{3.14 \times 4} \][/tex]
Calculate the denominator first:
[tex]\[ 3.14 \times 4 = 12.56 \][/tex]
Now divide the volume by this result:
[tex]\[ r^2 = \frac{314}{12.56} = 25 \][/tex]
To find [tex]\( r \)[/tex], take the square root of both sides:
[tex]\[ r = \sqrt{25} \][/tex]
[tex]\[ r = 5 \][/tex]
Therefore, the radius of the bucket, to the nearest whole number, is:
[tex]\[ \boxed{5 \text{ inches}} \][/tex]
So, the correct answer is:
A. 5 inches
