Explanation Given: The total surface area of a cylindrical water heater is 4170 sq. in. and height of the heater is 75 in. Definition used: Standard quadratic equation : “An equation in which the variable appears to the second power, but to no higher power, is called a quadratic equation. A standard quadratic equation can be expresses as, a x 2 ︸ + b x ︸ + c ︸ = 0 ↓ ↓ ↓ [ x 2 -term ] [ x -term ] [ Constant term ] That is every quadratic equation must have x 2 -term, but the x -term or constant tem may be missing.” Procedure used: 1. Identify the values of a , b and c by comparing the given equation with the standard quadratic equation a x 2 + b x + c = 0 . 2. Substitute the values of a , b and c into the quadratic equation formula x = − b ± b 2 − 4 a c 2 a . 3. Simplify the equation for x . 4. Check the solution by back substituting the values of x in the original equation. Calculation: Consider r and h as the radius and height of the water heater, respectively. Note that the total surface area of a cylinder is 2 π r 2 + 2 π r h . Given area of the TSA is 4170 sq. in and height is 75 in. So, substitute 4170 for TSA and 75 for height in the above formula as follows. TSA = 2 π r 2 + 2 π r h 4170 = 2 π r 2 + 2 π r ( 75 ) 2 π r 2 + 150 π r − 4170 = 0 6.2832 r 2 + 471.24 r − 4170 = 0 Thus, the standard quadratic equation is 6.2832 r 2 + 471.24 r − 4170 = 0 . Step 1: Identify the values of a , b and c by comparing the given equation with the standard quadratic equation a r 2 + b r + c = 0 . 6.2832 r 2 ︸ + 471

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Author: SAUNDERS

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Chapter 11.2, Problem 11CE

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To find: The radius of a cylindrical water heater.

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The radius of a cylindrical water heater.

Solution Summary: The author calculates the radius of a cylindrical water heater by comparing the given equation with the standard quadratic equation.

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To find: The radius of a cylindrical water heater.

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Chapter 11 Solutions