​ A Concrete Reservoir in the Shape of a Triangular Prism

question 199

Short Answer

​
A concrete reservoir in the shape of a triangular prism is being filled with water at the constant rate of 1 cubic feet per minute.The reservoir is 4 feet deep,measures 6 feet across the top,and is 30 feet long,as shown in the figure below.For any time ,let represent the depth of the water in the reservoir,and let represent the width of the rectangular region of water at the top.
​ a = 30 ft
b = 6 ft
c = 4​ ft
​
-​If the reservoir is initially empty,how long will it take to fill completely? Round your answer to the nearest whole number.

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Definitions:

Prehensility

The ability of certain body parts, like tails or fingers, to grasp or hold objects, often seen in primates and some other animals.

Brachiation

Moving from branch to branch using the arms, with the body hanging suspended below.

Manipulate Objects

the ability to control and move items in the environment using physical contact, typically involving hands or tools.

Gorillas

Large apes native to the forests of central Sub-Saharan Africa, known for their intelligence and complex social structures.