Q:

# A cylindrical container is used to hold drinking water on the sidelines for a football team. The maximum capacity of the container is 26,460 mL. If the height of the container is 60 cm, what is the radius of the cylinder? (1 mL = 1 cm3) A. 21 cm B. 7.35 cm C. 220.5 cm D. 42 cm

Accepted Solution

A:
To solve this we are going to use the formula for the volume of a cylinder: $$V= \pi r^2h$$
where
$$V$$ is the volume of the cylinder in cube centimeters
$$r$$ is the radius of the cylinder in centimeters
$$h$$ is the height of the cylinder in centimeters

We know for the problem that volume of our cylinder is 26,460 mL. Since 1 mL =$$1cm^3$$, the volume of our cylinder is $$26460cm^3$$. We also know for our problem that the height of our cylinder is 60 cm, so $$h=60$$. Lets replace those values in our formula and solve for $$r$$:
$$V= \pi r^2h$$
$$26460= \pi r^2(60)$$
$$26460=60 \pi r^2$$
$$r^2= \frac{26460}{60 \pi }$$
$$r^2= \frac{441}{ \pi }$$
$$r= \sqrt{ \frac{441}{ \pi } }$$
$$r= \frac{21}{ \sqrt{ \pi } }$$
$$r=11.8$$

We can conclude that the radius of the football team's cylindrical container is 11.8 cm