Question

consider a rectangular prism container that is initially empty. the container has base dimensions of 5m x 3m, and a height of 4m. 5000 gallons of water is added to the container. the height of the water above the containers base is ___ft. note: • submit your answer to 3 significant digits. your answer: 4.14 answer question 2 (1 point) saved ...continuing from #1... a solid concrete cube (30in x 30in x 30in) is slowly placed at the bottom of the container. the height of the water above the containers base is ___ft. note: • submit your answer to 3 significant digits. your answer:

Explanation:

Step1: Convert gallons to cubic - feet

1 gallon = 0.133681 cubic - feet. So, 5000 gallons of water is $V_{water}=5000\times0.133681 = 668.405$ cubic - feet.

Step2: Calculate the base area of the container in square - feet

The base dimensions of the container are $5m\times3m$. Since 1m = 3.28084 feet, the base area $A=(5\times3.28084)\times(3\times3.28084)=16.4042\times9.84252 = 161.475$ square - feet.

Step3: Find the initial height of water in the container

Using the formula $V = A\times h$, we can find the height of water $h_1=\frac{V_{water}}{A}=\frac{668.405}{161.475}\approx4.14$ feet.

Step4: Convert the side - length of the cube to feet

The side - length of the cube is 30 inches. Since 1 inch = 0.0833333 feet, the side - length $s = 30\times0.0833333=2.5$ feet.

Step5: Calculate the volume of the cube

The volume of the cube $V_{cube}=s^3=(2.5)^3 = 15.625$ cubic - feet.

Step6: Calculate the new volume of water and cube combined

$V_{total}=V_{water}+V_{cube}=668.405 + 15.625=684.03$ cubic - feet.

Step7: Find the new height of water

Using $V = A\times h$ again, $h_2=\frac{V_{total}}{A}=\frac{684.03}{161.475}\approx4.24$ feet.

Answer:

4.24