Mathematics
vincentaemeterio
3

how many cubic blocks with a side length of 1/8 inch are needed to fill a rectangular prism with a length width and height of 3/4 inch 1/2 inch and 1/2 inch

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(1) Answers
Kip

First lets calculate the total volume of the rectangular prism: volume = length*width*height v = (3/4)(1/2)(1/2) = (3*1*1)/(4*2*2) = 3/16 so the total volume of the prism is 3/16 cubic inches, now we need to know how many cubic blocks of 1/8 inch side length fill the 3/16 volume, that is solved by finding a number that multiplied by the volume of a cubic block of side 1/8 gives us 3/16, lets call the number x and write the respective equation: the volume of the cubic block is (1/8)(1/8)(1/8) = 1/(8*8*8) = 1/512, therefore: (1/512)x = 3/16 solving for x: x = (3/16)*512 = 3*512/16 x = 96 so you need 96 cubic blocks of 1/8 inch sides to fill the stated prism

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