Explanation Given Information: The amount of water emptied by a pipe is directly proportional to the square of the diameter of the pipe. A pipe of diameter 6 in empties 200 gal of water into the canal in an hour. The water level is same or constant. Formula used: If y varies directly as square of x , then by definition of direct variation, there exists a real number k such that, y = k x 2 The variation problem is solved using following steps. Step 1: Define the given variables and frame the variation equation. Step 2: Calculate the value of the constant of variation k using given information. Step 3: Use value of k from Step 2 to rephrase the variation equation. Step 4: Calculate the unknown by substituting the remaining values and find required result. Calculation: Consider a pipe of diameter 6 in which empties 200 gal of water into the canal in an hour. The amount of water emptied by a pipe of diameter 12 in into the canal in an hour is calculated as, Firstly, define the variables as, A = Amount of water emptied d = diameter of pipe Frame the variation equation, As the amount of water emptied by a pipe is directly proportional to the square of the diameter of the pipe, by the definition of direct variation, the variation equation is, A = k d 2 Here, k is the constant of variation. To find the value of the constant of variation, use the provided information that pipe of diameter 6 in empties 200 gal of water into the canal in an hour. Substitute A = 200 and d = 6 in A = k d 2

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Author: Lial

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Chapter 9.4, Problem 52E

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Chapter 9.4, Problem 51E

Chapter 9.4, Problem 53E

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Chapter 9 Solutions

INTEGRATED REV.F/BEG.+INT.ALG.W/ACC.>C<

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The amount of water emptied by a pipe of diameter 12 in into the canal in an hour.

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