when it rains, a large rain barrel fills with water at an average rate of 25 gallons per minute. the diagram…

when it rains, a large rain barrel fills with water at an average rate of 25 gallons per minute. the diagram shows the dimensions of the rain barrel. how long, to the nearest minute, will it take the rain barrel to fill with water to 40% of its capacity? use 1 gallon = 231 cubic inches. enter the answer in the box. minutes

when it rains, a large rain barrel fills with water at an average rate of 25 gallons per minute. the diagram shows the dimensions of the rain barrel. how long, to the nearest minute, will it take the rain barrel to fill with water to 40% of its capacity? use 1 gallon = 231 cubic inches. enter the answer in the box. minutes

Answer

Explanation:

Step1: Calculate the volume of the cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$. The radius $r = \frac{60}{2}=30$ inches and height $h = 80$ inches. So $V=\pi\times30^{2}\times80=72000\pi$ cubic - inches.

Step2: Find 40% of the volume

$V_{40%}=0.4\times72000\pi = 28800\pi$ cubic - inches.

Step3: Convert the volume from cubic - inches to gallons

Since 1 gallon = 231 cubic - inches, the volume in gallons is $V_{gallons}=\frac{28800\pi}{231}\approx\frac{28800\times3.14}{231}\approx391.7$ gallons.

Step4: Calculate the time

The filling rate is 25 gallons per minute. Using the formula $t=\frac{V}{r}$, where $V$ is the volume and $r$ is the rate. So $t=\frac{391.7}{25}=15.668\approx16$ minutes.

Answer:

16