A fish tank 24 inches long, 16 inches wide, and 12 inches high is 3/4 full of water. By how many inches will the water level rise if you should add 576 cubic inches of water?
One inch of water in this tank contains 384 cubic inches.
576 / 384 = 1.5 inches
Ms. Sue's insight into this problem was much better than mine and it was cleverly done. If you want to do it the brute force method, which I used, it follows.
Volume of tank = 24x16x12 = 4608 in^3.
3/4 full means it has 4608x(3/4) = 3456 in^3 water in it.
24 x 16 x ??height = 3456 and solve for ?? (the height). That is 3456/(24x16) = 9 inches is the initial height of the water. (That agrees with Ms. Sue's number of 384 for 1" and 384 x 9" = 3456 in^3.
Now we add 576 in^3 to the tank containing 3456 to give a volume of 4032 in^3, then
24 x 16 x ??height = 4032.
height = 4032/(24x16) = 10.5"
So the new height is 10.5", the initial height was 9" so 10.5-9=1.5 inch rise in the water level. (I didn't say it was shorter this way, did I?).
gfh
- square root of 85
The outside of an ice chest is 24 inches across, 14 inches wide, and 16 inches high. All sides of the ice chest have an insulating layer that has a uniform width of x inches. The inner volume of the ice chest is 3003 cubic inches.
To find out by how many inches the water level will rise, we need to determine the change in volume. Since the fish tank is already 3/4 full of water, we first need to calculate the current volume of water in the tank.
To find the volume of a rectangular prism (fish tank), we multiply its length, width, and height. In this case, the length is 24 inches, the width is 16 inches, and the height is 12 inches.
Volume of the fish tank = length × width × height
= 24 inches × 16 inches × 12 inches
= 4608 cubic inches
Since the tank is 3/4 full, the current volume of water in the tank is 3/4 of the total volume of the tank.
Current water volume = (3/4) × 4608 cubic inches
= 3456 cubic inches
Now, we can find the change in volume by adding 576 cubic inches to the current water volume.
Change in volume = Current water volume + 576 cubic inches
= 3456 cubic inches + 576 cubic inches
= 4032 cubic inches
Finally, we can calculate the rise in water level by dividing the change in volume by the area of the base of the tank. The area of the base is obtained by multiplying the length and width of the tank.
Area of the base = length × width
= 24 inches × 16 inches
= 384 square inches
Rise in water level = Change in volume / Area of the base
= 4032 cubic inches / 384 square inches
= 10.5 inches (rounded to one decimal place)
Therefore, if you add 576 cubic inches of water to the fish tank, the water level will rise by approximately 10.5 inches.