Use the image to answer the question.
An illustration shows a 3 D rectangular cuboid segmented into multiple blocks. It shows two adjacent sets of a 3 row by 6 column grid. The width is start fraction 1 over 2 end fraction, the length is 1 start fraction one over 2 end fraction, and the height is start fraction 3 over 4 end fraction.
Multiply the edge lengths of a right rectangular prism with length 1/2, width 1 1/2, and height 3/4 to show that the product is the same as the volume you found by packing the prism with unit cubes with an edge length of 1/4 inch.
Cube method:
Number of cubes: 36
Volume of each cube: 1/4×1/4×1/4=1/64
Volume of the prism:
v=36×1/64
=36/64
=9/16 cubic units
(1 point)
Responses
12×112×34
Start Fraction 1 over 2 End Fraction times Start Fraction 11 over 2 End Fraction times Start Fraction 3 over 4 End Fraction
12×32×34
Start Fraction 1 over 2 End Fraction times Start Fraction 3 over 2 End Fraction times Start Fraction 3 over 4 End Fraction
12×32×32
Start Fraction 1 over 2 End Fraction times Start Fraction 3 over 2 End Fraction times Start Fraction 3 over 2 End Fraction
12×12×34
Start Fraction 1 over 2 End Fraction times Start Fraction 1 over 2 End Fraction times Start Fraction 3 over 4 End Fraction
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12×32×34
Start Fraction 1 over 2 End Fraction times Start Fraction 3 over 2 End Fraction times Start Fraction 3 over 4 End Fraction
=1/2 x 3/2 x 3/4
= 9/16
So, the product of the edge lengths of the rectangular prism is the same as the volume found by packing the prism with unit cubes with an edge length of 1/4 inch.