Question

The volume of a cylinder is 770 cm°. It has a height of5 cm. Find its radius.

Answer 1

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:

`V=\pi r^2h`

Since we will need the radius, we solve for r:

`\begin{gathered} (V)/(\pi h)=r^2 \\ \boxed{\sqrt{(V)/(\pi h)}=r} \end{gathered}`

Step 3. Using the previous formula to find r by substituting the known values:

`\begin{gathered} r=\sqrt{(770cm^(^3))/(\pi(5cm))} \\ Using \\ \pi=3.1416 \\ r=\sqrt{(770cm^(^3))/((3.1416)(5cm))} \end{gathered}`

Solving the operations:

`\begin{gathered} r=\sqrt{(770cm^3)/(15.708cm)} \\ r=√(49.01961cm^2) \\ r=7.0014cm \end{gathered}`

The radius is 7.0014 cm (which can be rounded to 7cm)

Answer:

`\begin{gathered} Radius: \\ 7.0014cm \end{gathered}`