Question

a farmer is filling their circular water tank, which has a diameter of 8 meters and a depth of 3 meters. if 1 cubic meter is about 264 gallons, and the water pump has a flow rate of 45 gallons per minute, how long will it take to fill the tank? use the formula for the volume of the cylinder, $v = pi r^{2}h$, where $r$ is the radius (half the diameter), and $h$ is the depth. move one answer to each box to complete the sentences. the volume of the circular water tank is. multiply the volume of the tank by to find the volume in gallons. then, multiply the volume in gallons by to find the number of minutes it takes to fill the circular water tank. convert the time in minutes to to have a more reasonable answer.

Explanation:

Step1: Calculate the radius

Given diameter $d = 8$ meters, so $r=\frac{d}{2}=\frac{8}{2}=4$ meters, and $h = 3$ meters. Using the volume formula $V=\pi r^{2}h$, we get $V=\pi\times4^{2}\times3=48\pi$ cubic - meters.

Step2: Convert to gallons

Since 1 cubic - meter is about 264 gallons, to convert the volume from cubic - meters to gallons, we multiply the volume in cubic - meters by 264.

Step3: Calculate the time in minutes

The pump has a flow rate of 45 gallons per minute. Let $t$ be the time in minutes. If the volume in gallons is $V_{g}$, then $t=\frac{V_{g}}{45}$, which is equivalent to multiplying the volume in gallons by $\frac{1}{45}$.

Step4: Convert to a more reasonable unit

The resulting time in minutes may be a large number, so converting it to hours (since 1 hour = 60 minutes) gives a more reasonable - sized answer.

Answer:

The volume of the circular water tank is $48\pi$ cubic - meters. Multiply the volume of the tank by $264$ to find the volume in gallons. Then, multiply the volume in gallons by $\frac{1}{45}$ to find the number of minutes it takes to fill the circular water tank. Convert the time in minutes to hours to have a more reasonable answer.