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What must be the height of a cylindrical 750-gallon tank if it is 4 feet in diameter? (1 cubic foot = 7.48 gallons) Round to the nearest inch.

Answer :

Final answer:

The height of a cylindrical tank with a diameter of 4 feet that can hold 750 gallons of liquid is approximately 96 inches.

Explanation:

The student is essentially asking for the height of a cylindrical tank capable of holding 750 gallons of liquid, given that the tank's diameter is 4 feet. To solve this, we use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, h is the height, and π is approximately 3.14159.

Firstly, convert the volume from gallons to cubic feet, using the conversion factor 1 cubic foot = 7.48 gallons. Thus, 750 gallons = 750/7.48 = 100.27 cubic feet. Secondly, we convert the diameter to radius (since the formula for volume needs radius, and radius is half of the diameter), so r = 4/2 = 2 feet. Then we solve the formula for h: h = V/πr² = 100.27/(3.14159 * 2²) = 7.96 feet. To convert this to inches (since we are asked to round to the nearest inch), we multiply by 12, to get 95.52 inches. Rounded to the nearest inch, the needed height of the tank is 96 inches.

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