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.

Question

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 6/4
=36/64
=9/16 cubic units

Answer 1

Edge lengths of the prism: 1/2, 3/2, 3/4

Multiplying the edge lengths:
(1/2) * (3/2) * (3/4)
= 1/4 * 3/4
= 3/16

This product, 3/16, represents the volume of the prism when calculated using the edge lengths.

Comparing it to the volume found by packing the prism with unit cubes with an edge length of 1/4 inch:
9/16 (volume of prism calculated using the cube method) = 3/16 (volume of prism calculated using edge lengths multiplied)

3/16 is the same as 9/16, confirming that both methods yield the same volume for the right rectangular prism.