document.write( "Question 1181985: a baking pan has an rectangular base 12 in by 8 in, the sides and ends of the pan slope outward, so that the upper edges measure respectively 13 1/2 in by 9 in. if the depth of the pan is 2 in, find the amount of cake batter requires to fill the pan to 1/2 its depth \n" ); document.write( "

Algebra.Com's Answer #812536 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "a baking pan has an rectangular base 12 in by 8 in, the sides and ends of the pan
\n" ); document.write( "slope outward, so that the upper edges measure respectively 13 1/2 in by 9 in.
\n" ); document.write( "if the depth of the pan is 2 in, find the amount of cake batter requires to fill
\n" ); document.write( "the pan to 1/2 its depth
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document.write( "The base dimensions are 12 in by 8 in.\r\n" );
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document.write( "The upper edges measures are  13.5 inches  by  9 inches.\r\n" );
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document.write( "Dimensions at the 1/2 of the depth are (obviously)  12 +  = 12.75 inches  by  8 +  = 8.5 inches.\r\n" );
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document.write( "It is not difficult to check that the shape under consideration is a pyramidal frustum.\r\n" );
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document.write( "Apply the formula for the volume of a pyramidal frustum \r\n" );
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document.write( "     V = .\r\n" );
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document.write( "Here h is the height of the frustum;  is the area of the top base face = 12.75*8.5 = 108.375 in^2;\r\n" );
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document.write( " is the area of the bottom base face = 12*8 = 96 in^2.\r\n" );
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document.write( "So, the volume is\r\n" );
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document.write( "    V =  = 102.125 cubic inches.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "On the pyramidal frustum volume formula see the link\r
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\n" ); document.write( "\n" ); document.write( "https://mathworld.wolfram.com/PyramidalFrustum.html\r
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\n" ); document.write( "\n" ); document.write( "https://mathworld.wolfram.com/PyramidalFrustum.html\r
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\n" ); document.write( "\n" ); document.write( "My answer differs from the answer by tutor @greenestamps.\r
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\n" ); document.write( "\n" ); document.write( "It is because one formula in the solution by @greenestamps needs to be corrected.\r
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\n" ); document.write( "\n" ); document.write( "This formula is for the volume of four pyramids in section (3) of the solution by @greenestamps\r
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\n" ); document.write( "\n" ); document.write( "Its correct form is\r
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\n" ); document.write( "\n" ); document.write( " $\"%284%29%28%281%2F3%29%28%28%281%2F4%29h%29%28%283%2F8%29h%29%29%29%28h%29+=+%281%2F8%29h%5E3\"$ \r
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\n" ); document.write( "\n" ); document.write( "without the factor $\"1%2F2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "With this correction, the solution by @greenestamps gives the same final answer of 102.125 in^3, as my solution.\r
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