Question

question 1 (1 point)
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:
answer
question 2 (1 point)
...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:

Explanation:

1. First, convert the volume of water from gallons to cubic - feet.

• 1 gallon = 0.133681 cubic - feet. So, 5000 gallons of water is \(V = 5000\times0.133681=668.405\) cubic - feet.
• The base area of the rectangular - prism container in square feet: The base dimensions are \(5m\times3m\). Since \(1m = 3.28084\) feet, the base dimensions in feet are \(5\times3.28084 = 16.4042\) feet and \(3\times3.28084 = 9.84252\) feet. The base area \(A=16.4042\times9.84252\approx161.47\) square feet.
• Using the formula \(V = A\times h\) (where \(V\) is volume, \(A\) is base - area, and \(h\) is height), we can find the height of the water \(h=\frac{V}{A}=\frac{668.405}{161.47}\approx4.14\) feet.

1. First, convert the side - length of the cube from inches to feet. Since \(1\) foot \( = 12\) inches, a \(30\) - inch side - length is \(s=\frac{30}{12}=2.5\) feet. The volume of the cube \(V_{cube}=s^{3}=(2.5)^{3}=15.625\) cubic feet.

• The new volume of the water and the cube together is \(V_{total}=668.405 + 15.625=684.03\) cubic feet.
• Using the base area \(A\approx161.47\) square feet and the formula \(V = A\times h\), the new height of the water \(h=\frac{V_{total}}{A}=\frac{684.03}{161.47}\approx4.24\) feet.

Answer:

(a) 4.14
(b) 4.24