Final answer:
To find the height of a 750-gallon cylindrical tank with a 4-foot diameter, convert gallons to cubic feet and use the formula V = πr²h to find the height, which is approximately 31.91 feet.
Step-by-step explanation:
To determine the height of a cylindrical 750-gallon tank with a diameter of 4 feet, we first need to use the conversion between gallons and cubic feet. To start, we need to know the conversion factor: 1 gallon is approximately 0.133681 cubic feet. Therefore, to convert 750 gallons to cubic feet, we would multiply 750 by 0.133681 to get the volume in cubic feet.
Volume in cubic feet = 750 gallons × 0.133681 cubic feet/gallon = 100.26075 cubic feet.
Since the volume (V) of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height, we can rearrange this formula to solve for the height (h). The radius of the tank is half its diameter, so radius = 2 feet / 2 = 1 foot.
Now, we can calculate the height:
h = Volume / (π × radius²)
= 100.26075 cubic feet / (3.14159 × (1 foot)²)
= 100.26075 cubic feet / 3.14159
= 31.91 feet (rounded to two decimal places).
Therefore, the height of the cylindrical tank must be approximately 31.91 feet to hold 750 gallons.