Answer:
Explanation:
Step 1: Recall the formula for the volume of a right rectangular prism: Volume = length x width x height.
Step 2: Note that we are given the height of the water tank (11 feet), but we need to find the length and width.
Step 3: Use the formula for the area of a rectangle to find the length and width of the top of the water tank. The area is given as 220 ft², so:Area = length x width
220 ft² = length x width.
Step 4: Find two numbers that multiply to 220 and also have a sum of 2 times the height (22 feet). One way to do this is to list the factor pairs of 220 and check the sums:1 x 220 = 220 (not a factor pair)2 x 110 = 220 (not a factor pair)4 x 55 = 220 (not a factor pair)5 x 44 = 220 (not a factor pair)10 x 22 = 220 (sum is 32)11 x 20 = 220 (sum is 31)20 x 11 = 220 (sum is 31)22 x 10 = 220 (sum is 32)Therefore, the length and width of the top of the water tank are 11 feet and 20 feet (or 20 feet and 11 feet).
Step 5: Plug in the values for the length, width, and height into the volume formula and solve:Volume = length x width x height
Volume = 11 ft x 20 ft x 11 ft
Volume = 2,420 ft³
the final answer: The volume of the water tank is 2,420 cubic feet.