Question

question 12 (multiple choice worth 1 points)
(volume mc)
an underground water storage tank is built in the shape of a triangular prism. the base of the triangle is 10 feet, and the height of the triangle is 13 feet. the height of the prism is 13
feet. if each cubic foot of water weighs 62.41 pounds, what is the weight of the water in the tank when it is at 90% capacity?
845 pounds
760.5 pounds
52,736.5 pounds
47,462.8 pounds

Explanation:

Step1: Calculate the area of the triangular base

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Given \(base = 10\) feet and \(height=13\) feet.
\(A=\frac{1}{2}\times10\times13 = 65\) square feet.

Step2: Calculate the volume of the triangular - prism tank

The formula for the volume of a prism is \(V=A\times h\) (where \(A\) is the base area and \(h\) is the height of the prism). Here, \(A = 65\) square feet and \(h = 13\) feet.
\(V=65\times13=845\) cubic feet.

Step3: Calculate the volume at 90% capacity

\(V_{90\%}=0.9\times845 = 760.5\) cubic feet.

Step4: Calculate the weight of the water

Since each cubic foot of water weighs \(62.41\) pounds, the weight \(W\) of the water is \(W=V_{90\%}\times62.41\).
\(W = 760.5\times62.41\approx47462.8\) pounds.

Answer:

47,462.8 pounds