Thursday, March 21, 2013

Volume of two blocks


Question: The first block has a base with a width of 5 inches and a length of 10 inches.  The height of the block is 15 inches.   The second block has a square base with all sides equal to 5 inches. What is the height of the second block if the volume of the second block is twice as large as the volume of the first block?

Answer:  The volume of the first block in cubic inches is


VFB=5x10x15


The volume of the second block in cubic inches is

VSB=5x5xh

Where h is the height of the second block

We know that the volume of the second block is twice as large as the volume of the first block.  This means that 2 times VFB is equal to the volume of the second block.


2x5x10x15=5x5xh


Divide each side by 5x5 to solve for h


h=(2x5x10x15)/(5x5)


Note that 10=2x5 and substitute 2x5 for 10 in the numerator of the expression for h.

Cancel 5x5 from both the numerator and the denominator and get

h=(2x2x15)=60


Check:  Check your answer by calculating the volume of both blocks and confirming that 2 times the volume of the first block equals the volume of the second block.  The volume of the first block is 750 cubic inches.  The volume of the second block is 1,500 cubic inches.  2x750=1,500.




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