A rectangular prism with a base area of 38 sq in & height of 9 in is filled to the top with water. The water is poured into fish tank that is 21 in by 8 in and is 10 in tall. How high is the water in the fish tank?
38 * 9 = 342 cubic inches
21 * 8 * x = 342
Solve for x.
To find the height of the water in the fish tank, we need to compare the volume of water in the rectangular prism to the volume of the fish tank.
Let's start by finding the volume of the rectangular prism. The volume of a rectangular prism is obtained by multiplying the base area by the height. In this case, the base area is 38 sq in and the height is 9 in.
Volume of the rectangular prism = base area * height
Volume of the rectangular prism = 38 sq in * 9 in
Volume of the rectangular prism = 342 cu in
Now, let's find the volume of the fish tank. The volume of a rectangular fish tank is determined by multiplying the length, width, and height. In this case, the length is 21 in, the width is 8 in, and the height is 10 in.
Volume of the fish tank = length * width * height
Volume of the fish tank = 21 in * 8 in * 10 in
Volume of the fish tank = 1680 cu in
Next, we'll compare the volumes to determine the height of the water in the fish tank. Since we know the volume of water in the rectangular prism is 342 cu in and the volume of the fish tank is 1680 cu in, we can set up a proportion.
Let "h" be the height of the water in the fish tank.
Volume of water / Volume of fish tank = Height of water in fish tank / Height of fish tank
342 cu in / 1680 cu in = h in / 10 in
Now, let's solve for "h".
342/1680 = h/10
Cross-multiplying, we get:
1680h = 342 * 10
1680h = 3420
h = 3420 / 1680
h ≈ 2.036
Therefore, the height of the water in the fish tank is approximately 2.036 inches.