Maths-
General
Easy

Question


The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces.
Water pours into the glass slowly and at a constant rate. Which of the following graphs best illustrates the height of the water level in the glass as it fills?

hintHint:

We will use logical thinking to solve this problem.

The correct answer is:


    Step 1 of 1:
    Water pours into the glass slowly and at a constant rate.
    Now, look into the picture of the glass and observe that the area of the glass increases as its height increases. So, as the water pours high in the glass the time will increase because of its increasing area.
    Area of the bottom of the glassequals pi cross times open parentheses k over 4 close parentheses squared equals fraction numerator pi k squared over denominator 16 end fraction
    Area of the top of the glassequals pi cross times open parentheses k over 2 close parentheses squared equals fraction numerator pi k squared over denominator 4 end fraction space of 1em therefore fraction numerator pi k squared over denominator 16 end fraction less than fraction numerator pi k squared over denominator 4 end fraction
    So, at first the water level rises fast for some time and then it rises slowly as if it takes more time. This all happens because of the constant rate of pouring water.
    Final Answer:
    The best illustrated graph should be —

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