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
