Question

Water drips into a cylindrical bucket with a diameter of 10 inches and a height of 16 inches. If water drips at a constant rate of 1/2 cubic inch per minute, how long will it take an empty bucket to be completely filled? Round to the nearest hour and minute.

A. 8 hours and 30 minutes
B. 10 hours and 40 minutes
C. 12 hours and 50 minutes
D. 15 hours and 5 minutes

Answer 1

It would take approximately 41 hours and 51 minutes for the bucket to be completely filled.

Step-by-step explanation:

To calculate the time it takes for the bucket to be completely filled, we need to find the volume of the bucket and divide it by the constant rate at which water drips. The equation for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. In this case, the diameter is given as 10 inches, so the radius is 5 inches. Plugging in the values, we get V = π(5^2)(16) = 400π cubic inches. As the water drips at a rate of 1/2 cubic inch per minute, it would take 400π / (1/2) = 800π minutes to fill the entire bucket. Rounding it to the nearest hour and minute, it would take approximately 2511 minutes, which is about 41 hours and 51 minutes.