How many gallons of water does a tank 20 feet high and circumference of 154 inches hold?


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David Shabazi answered

The tank is in the form of a cylinder, since it has a circular base with a given circumference, and a height.

Now, the question asks us to determine how many gallons of water can fit in this tank. This means we have to use the volume formula for a cylinder. Volume of a cylinder is π*(r^2)*h. But first, notice that the volume formula has the radius (r) variable in it. We're not given this value. But we ARE given circumference, and the formula for circumference has radius (r) in it. We can use that to determine what r is equal to.

C = 2πr = 154 in.

πr = 77 in.

r = 77/π in. Or 6.416/π ft. (since 1 ft = 12 in)

Now that we have our radius, we can plug this into the formula for volume of a cylinder.

V = π * (77/π)^2 * 240 (remember, 20 ft for height = 240 in for height because 1 ft = 12 in)

V = 240π * [5929/(π)^2] in^3 (the unit is to the power of 3 because we're finding out volume, which is 3-Dimensional space)

= 1,422,960/π in^3

This is in inches form. If you wanted the units in feet form, plug in the numbers with feet units instead of inch units:

V = π * (6.416/π)^2 * 20 ft^3

= 20π * (41.17/π^2) ft^3

= 823.3/π ft^3

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