multiply the edge length of right rectangular prism with length 1/2 width 1 1/2 and 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.

Answer 1

First, let's find the volume of the right rectangular prism using the given edge lengths.

Length = 1/2 inch
Width = 1 1/2 inches = 3/2 inches
Height = 3/4 inch

Volume = Length x Width x Height
Volume = (1/2) x (3/2) x (3/4)
Volume = 9/16 cubic inches

Now, let's calculate the volume of the prism by packing it with unit cubes with an edge length of 1/4 inch.

Since the edge length of the prism is 1/4 inch, each side of the prism can be divided into 2 segments of 1/4 inch each. Therefore, the prism can be seen as a 2x6x3 array of unit cubes.

Total number of unit cubes = 2 x 6 x 3 = 36

Volume = Total number of unit cubes x Volume of one unit cube
Volume = 36 x (1/4 x 1/4 x 1/4)
Volume = 36 x 1/64
Volume = 9/16 cubic inches

As shown above, both methods yield the same volume of 9/16 cubic inches. This demonstrates that the product of the edge lengths of the right rectangular prism is equivalent to the volume found by packing the prism with unit cubes.