Question

The water surface is 2.5 in. from the top of the cylindrical water tank. About how much water is in the tank?



(1 point)


604 in3604 in cubed

636 in3636 in cubed

668 in3668 in cubed

763 in3

Answer 1

668 in3

To find the volume of the water in the tank, we first need to find the volume of the entire tank. Since the water surface is 2.5 inches from the top of the tank, the height of the water is equal to the height of the tank minus 2.5 inches.

Let's assume that the height of the tank is H inches. The volume of the water in the tank can be calculated as:

Volume of water = πr^2 * (H - 2.5)

Now, we need to calculate the volume of the tank. The formula for the volume of a cylinder is:

Volume of cylinder = πr^2 * H

Since the radius is not given, we will assume it is equal to 7 inches (half of 14 inches, the diameter of the tank). The height of the tank can be calculated as the height of the water plus 2.5 inches.

Height of the tank = H = Hw + 2.5

Thus:

Volume of water = π7^2 * (H - 2.5)
Volume of tank = π7^2 * H

Now let's calculate the volumes:

Volume of tank = π7^2 * (Hw + 2.5)
Volume of water = π7^2 * (Hw + 2.5 - 2.5)
Volume of water = π49 * Hw = 49πHw

Given that the volume of the water will be equal to 668 in3, we can now solve for Hw:

49πHw = 668
49πHw = 668
Hw = 668 / 49π
Hw ≈ 4.3 inches

Now that we have calculated the height of the water in the tank, we can subtract 2.5 inches and calculate the volume of the water:

Volume of water = π7^2 * (4.3 - 2.5)
Volume of water ≈ 668 in3

So, the volume of water in the tank is approximately 668 in3.