Question

The volume of a cylinder is 1470pi cmcubed. The height of the cylinder is 30 cm. What is the radius of the​ cylinder?

Answer 1

To find the radius of a cylinder given its volume and height, we can use the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

Given:
- \( V = 1470\pi \) cm³
- \( h = 30 \) cm

We can substitute these values into the formula:

\[
1470\pi = \pi r^2 (30)
\]

Next, we can divide both sides by \( \pi \) (assuming \( \pi \) is not zero):

\[
1470 = r^2 (30)
\]

Now, we can solve for \( r^2 \) by dividing both sides by 30:

\[
r^2 = \frac{1470}{30}
\]

Calculating the right-hand side:

\[
r^2 = 49
\]

Now, to find \( r \), we take the square root of both sides:

\[
r = \sqrt{49} = 7 \text{ cm}
\]

Thus, the radius of the cylinder is \( \boxed{7} \) cm.