Question

Caleb is playing outside when he discovers a cylindrical well about 6 feet across. He is not sure how deep it is, so he decides to get a hose and fill it up. He puts about 400 cubic feet of water in the cylinder. About how deep must it be (height)?

A. 10 feet
B. 5 feet
C. 14 feet
D. 113 feet

Answer 1

Using the volume formula for a cylinder, the well's depth is found to be approximately 14 feet to accommodate the 400 cubic feet of water used to fill it.

To determine how deep the well is given the volume of water used to fill it, we can use the formula for the volume of a cylinder, which is V = πr^2h, where V is the volume, r is the radius, and h is the height or depth in this case. The diameter is 6 feet, so the radius is 6/2 = 3 feet. Plugging the known values into the formula, we have 400 = π(3)^2h. Solving for h, we get
h ≈ 14.15 feet. Therefore, the closest depth to the options given is 14 feet (Option C).

The depth of the well is approximately 14 feet based on the volume of water Caleb used to fill it.