document.write( "Question 1159719: A water storage tank has the shape of a cylinder with diameter 22 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 15 ft, what percentage of the total capacity is being used? (Round your answer to one decimal place.)
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Algebra.Com's Answer #782782 by greenestamps(13203)![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "72.6%. \n" ); document.write( "The answer is of little use to you, unless you just want to answer the question without learning anything. \n" ); document.write( "So I will tell you one way you can get that answer and let you have the experience of working the problem yourself. \n" ); document.write( "Draw a sketch of the cross section of the tank. It will be a circle with radius 11 with a horizontal chord 4 units above the middle of the circle. (The depth of the water is 15ft; the radius of the tank is 11ft; the chord representing the water level is 4ft above the center). \n" ); document.write( "Draw the radii to the two endpoints of the chord. \n" ); document.write( "A radius of the tank to one end of the chord forms a right triangle, allowing you to determine the length of the chord. (In that triangle, one leg is half of the chord; the other leg is 4ft and the hypotenuse is 11ft.) \n" ); document.write( "The area of the cross section of the tank that is water can be viewed as composed of two parts: (a) the area of the triangle formed by the chord and the two radii to the ends of the chord; and (b) the sector of the circle \"below\" those two radii. \n" ); document.write( "At this point you know the measures of the legs of the triangle, so you can easily determine its area. \n" ); document.write( "For the sector of the circle, observe that the angle above the midline of the cross section is \n" ); document.write( "The next-to-last step is to add the areas of the triangle and the sector of the circle; the last step is to convert that to a percentage by dividing that area by the area of the whole circle. \n" ); document.write( " \n" ); document.write( " |