Answer: 125.66 cubic inches.
Step-by-step explanation: The formula for the volume of a cylinder is:
[tex][ V = \pi \cdot r^2 \cdot h ][/tex]
where:
(V) represents the volume of the cylinder.
(\pi) (pi) is approximately 3.14159.
(r) is the radius of the base.
(h) is the height of the cylinder.
We’re given that the circumference of the cylinder is 314 inches. The circumference ((C)) of a circle is related to its radius ((r)) as follows:
[tex][ C = 2\pi r ][/tex]
Solving for (r):
[tex][ r = \frac{C}{2\pi} ][/tex]
Now let’s find the radius:
[tex][ r = \frac{314}{2\pi} ][/tex]
Using a higher level of precision for (\pi), we get:
[tex][ r \approx \frac{314}{2 \cdot 3.14159} \approx 50 ][/tex]
Next, we can calculate the volume:
[tex][ V = \pi \cdot r^2 \cdot h ] [ V = 3.14159 \cdot (50)^2 \cdot 4 ] [ V \approx 125.6637 , \text{cubic inches} ][/tex]
Therefore, the volume of the cylinder with a height of 4 inches and a circumference of 314 inches is approximately 125.66 cubic inches.
hope this helps ^^ (very much appreciated w/ a brainliest answer) <3