To determine the radius of the cylindrical bucket, we need to solve the formula for the volume of a cylinder. The formula is given by:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( \pi \)[/tex] is a constant (approximately 3.14),
- [tex]\( r \)[/tex] is the radius,
- [tex]\( h \)[/tex] is the height.
We are given:
- Volume [tex]\( V = 314 \)[/tex] cubic inches,
- Height [tex]\( h = 4 \)[/tex] inches,
- [tex]\( \pi \approx 3.14 \)[/tex].
First, we need to solve for [tex]\( r \)[/tex], the radius. Start with the original formula:
[tex]\[ 314 = 3.14 \cdot r^2 \cdot 4 \][/tex]
Let's isolate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = \frac{314}{3.14 \times 4} \][/tex]
Now, perform the operations inside the fraction:
[tex]\[ 3.14 \times 4 = 12.56 \][/tex]
So,
[tex]\[ r^2 = \frac{314}{12.56} \][/tex]
Next, divide 314 by 12.56:
[tex]\[ r^2 = 25.0 \][/tex]
To find [tex]\( r \)[/tex], take the square root of both sides:
[tex]\[ r = \sqrt{25.0} \][/tex]
[tex]\[ r = 5.0 \][/tex]
Thus, the radius [tex]\( r \)[/tex] is [tex]\( 5.0 \)[/tex] inches.
Since we are asked for the radius to the nearest whole number, we round 5.0 to the nearest whole number:
[tex]\[ r \approx 5 \][/tex]
Therefore, the radius of the bucket, to the nearest whole number, is 5 inches.
The correct answer is:
C. 5 inches
