document.write( "Question 1137310: Find the capacity in litres of a bucket of 24cm at the top ,16cm at the bottom and 18cm deep.Pls i need a diagram to support the solution \n" ); document.write( "

Algebra.Com's Answer #755182 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "I will assume that the basket has circular section; in other word, I will assume that the basket is a part of circular cone;
\n" ); document.write( "this part is called \"a frustum of a cone\".\r
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\n" ); document.write( "\n" ); document.write( "There are two ways to solve this problem.\r
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\n" ); document.write( "\n" ); document.write( "One way is to apply the formula for the volume of the frustum of a cone.
\n" ); document.write( "If you don't know or do not remember this formula (as I myself do not remember it, for example), you can easily
\n" ); document.write( "find it in the Internet, searching GOOGLE with keyword \"volume frustum cone\".\r
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\n" ); document.write( "\n" ); document.write( "Another way it to think a bit and to reduce this formula on your own, leaning on the knowledge about a cone volume
\n" ); document.write( "that you get from the school.\r
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\n" ); document.write( "\n" ); document.write( "I will show you both ways.\r
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\n" ); document.write( "\n" ); document.write( "Solution 1. Using the formula\r
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document.write( "This way is shorter; therefore, I will start this way.\r\n" );
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document.write( "The formula for the volume of the frusrum of a cone is\r\n" );
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document.write( "     = \r\n" );
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document.write( "where R is the radius of the larger base; r is the radius of the shorter base and h is the frustum height.\r\n" );
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document.write( "    See this Internet site  \r\n" );
document.write( "    http://jwilson.coe.uga.edu/emt725/frustum/frustum.cone.html\r\n" );
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document.write( "    where you will find the diagram of a frustum, too.\r\n" );
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document.write( "Now substitute the given data  R = 24/2 = 12 cm,  r = 16/2 = 8 cm and h = 18 cm into the formula\r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "and calculate.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The other way requires more explanations and more writing from me.\r
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\n" ); document.write( "\n" ); document.write( "Solution 2\r
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document.write( "Each and every frustum of a cone is a part of some cone.\r\n" );
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document.write( "In particular, the given basket is a part of some cone.\r\n" );
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document.write( "What cone is it, in your case ?\r\n" );
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document.write( "Imagine that you increased the height from 18 to 36 centimeters, remaining the base size of 24 cm unchangeable.\r\n" );
document.write( "Then, obviously, the smaller base will be 8 cm in diameter.\r\n" );
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document.write( "Imagine that you increased the height for another 18 cm, from 36 to 54 centimeters, remaining the base size of 24 cm unchangeable.\r\n" );
document.write( "Then, obviously, you will get the full cone (!).\r\n" );
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document.write( "Thus, the full cone has the height of 54 centimeters and the base diameter of 24 cm.\r\n" );
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document.write( "Your basket is what will remain from this cone, when you cut the upper part by the plane parallel to its base \r\n" );
document.write( "at the distance of 18 cm from the base.\r\n" );
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document.write( "It gives you the formula for the frustum volume\r\n" );
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document.write( "     = V(large cone) - V(small cone to cut) =\r\n" );
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document.write( "                     =  -  = .\r\n" );
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document.write( "Again, use your calculator.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I just completed my explanations.\r
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\n" ); document.write( "\n" ); document.write( "I hope that after calculating the answers from both solutions, you will compare the results.
\n" ); document.write( "I also hope that these results will be the same.\r
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\n" ); document.write( "\n" ); document.write( "Finally, I hope that when you complete this assignment, you will post your \"Thanks\" to me.\r
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