To find the radius of a right cylindrical container, we can use the formula for the volume of a cylinder. The formula is given by:
V = πr^2h
where V is the volume of the cylinder, r is the radius of its base, and h is its height.
We are given that the height \( h \) of the cylinder is 5 inches and the volume \( V \) is \( 245 \pi \) cubic inches. Now we can plug these values into the volume formula to solve for r.
\( 245 \pi = \pi r^2 \cdot 5 \)
First, we can simplify by dividing both sides of the equation by \( \pi \):
\( 245 = r^2 \cdot 5 \)
Next, we divide both sides by 5:
\( \frac{245}{5} = r^2 \)
\( 49 = r^2 \)
Finally, we take the square root of both sides to solve for r:
\( \sqrt{49} = r \)
\( r = 7 \)
So, the radius of the container is 7 inches.
