a cylindrical barrel is 2.8 feet in diameter and 8 feet high. if a cubic foot holds about 7.5 gallons of liquid how many gallons of water will this barrel hold?

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To find the number of gallons of water that a cylindrical barrel can hold, we need to calculate the volume of the barrel in cubic feet and then convert it into gallons.

First, let's calculate the volume of the barrel using the formula for the volume of a cylinder: V = πr^2h, where V represents the volume, r is the radius, and h is the height.

Given that the diameter of the barrel is 2.8 feet, we can find the radius by dividing the diameter by 2: r = 2.8 ft / 2 = 1.4 ft.

The height of the barrel is given as 8 feet.

So, the volume of the barrel is: V = π(1.4 ft)^2 * 8 ft.

Now we can calculate the value of the volume. However, since π (pi) is an irrational number, we can use an approximation of π as 3.14 for our calculation:

V ≈ 3.14 * (1.4 ft)^2 * 8 ft.
V ≈ 3.14 * 1.96 ft^2 * 8 ft.
V ≈ 49.088 ft^2 * 8 ft.
V ≈ 392.704 ft^3.

Now, we need to convert the volume from cubic feet to gallons. Given that 1 cubic foot is approximately equal to 7.5 gallons, we can multiply the volume by this conversion factor:

392.704 ft^3 * 7.5 gallons/ft^3 ≈ 2945.28 gallons.

Therefore, the cylindrical barrel can hold approximately 2945.28 gallons of water.