Step 1. The information that we have about the cylinder is:
And we need to find the radius r.
Step 2. The formula for the volume of a cylinder is:
[tex]V=\pi r^2h[/tex]
Since we will need the radius, we solve for r:
[tex]\begin{gathered} \frac{V}{\pi h}=r^2 \\ \boxed{\sqrt{\frac{V}{\pi h}}=r} \end{gathered}[/tex]
Step 3. Using the previous formula to find r by substituting the known values:
[tex]\begin{gathered} r=\sqrt{\frac{770cm^{^3}}{\pi(5cm)}} \\ Using \\ \pi=3.1416 \\ r=\sqrt{\frac{770cm^{^3}}{(3.1416)(5cm)}} \end{gathered}[/tex]
Solving the operations:
[tex]\begin{gathered} r=\sqrt{\frac{770cm^3}{15.708cm}} \\ r=\sqrt{49.01961cm^2} \\ r=7.0014cm \end{gathered}[/tex]
The radius is 7.0014 cm (which can be rounded to 7cm)
Answer:
[tex]\begin{gathered} Radius: \\ 7.0014cm \end{gathered}[/tex]
