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 12 , width 112 , and height 34 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 14 inch.
Cube method:
Number of cubes: 36
Volume of each cube: 14×14×14=164
Volume of the prism:
v=36×1/64
=36/64
=9/16 cubic units
(1 point)
Responses
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
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
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12×32×34
This calculation would be:
Start Fraction 1 over 2 End Fraction times 3 times Start Fraction 3 over 4 End Fraction
Multiplying these values would give us the product: 192
Therefore, the volume found by packing the prism with unit cubes of edge length 14 inches is the same as the product of the edge lengths of the rectangular prism.