document.write( "Question 1205029: A heavy cube of side 8cm is placed vertically in a cylindrical tank of radius 7cm which contains water.
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\n" ); document.write( "A heavy cube of side 8 cm is placed vertically in a cylindrical tank of radius 7 cm which contains water.
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document.write( "(a)  In this case, the entire cube is wholly submerged into the water in the tank.\r\n" );
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document.write( "     The water level rises over the entire base area of the cylindrical tank.\r\n" );
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document.write( "     The raised water represents the volume of the displaced water in the tank by the solid cube.\r\n" );
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document.write( "             Use the law of the volume of water conservation.\r\n" );
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document.write( "     To find the rise for question (a), we should divide the volume of the cube,   cm^3\r\n" );
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document.write( "     by the area of the base of the cylinder\r\n" );
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document.write( "         the rise =  =  = 3.326 cm.\r\n" );
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document.write( "     ANSWER to question (a).  The rise of the water level is 3.326 cm.\r\n" );
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document.write( "(b)  In this case, the cube is only partly submerged into the water in the tank.\r\n" );
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document.write( "     The water level rises over the part of the base area of the cylindrical tank.\r\n" );
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document.write( "     This part of the area where the water rises is the entire area of the base of the tank \r\n" );
document.write( "     minus the area of the base of the cube, which is only partially submerged.\r\n" );
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document.write( "             Use the law of the volume of water conservation.\r\n" );
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document.write( "     To find the new level of water for question (b), we should divide the volume of the water in the tank,  \r\n" );
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document.write( "     which is   cm^3, by the (area of the tank base MINUS area of the cube base)\r\n" );
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document.write( "         the new level =  = 3.4232 cm  (rounded).\r\n" );
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document.write( "     Thus the raise of the water level is  3.4232 - 2 = 1.4232 centimeters.\r\n" );
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document.write( "     The new level is still lower than the height of the cube, so our calculations make sense.\r\n" );
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document.write( "     ANSWER to question (b).  The rise of the water level is 3.4232 cm.\r\n" );
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