Question
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 1/4 x 1/4 x1/4 = 1/64 Volume of the prism v =36 x 1/64 = 36/64 = 9/16 cubic units
Answers
GPT 3.5
Edge lengths of the prism: length = 1/2, width = 3/2, height = 3/4
Volume of the prism = length x width x height
= (1/2) x (3/2) x (3/4)
= 9/16
Now let's calculate the volume using the cube method:
Number of cubes = 36
Volume of each cube = (1/4) x (1/4) x (1/4) = 1/64
Total volume = 36 x 1/64 = 9/16
Therefore, both methods give the same volume of 9/16 cubic units.
Volume of the prism = length x width x height
= (1/2) x (3/2) x (3/4)
= 9/16
Now let's calculate the volume using the cube method:
Number of cubes = 36
Volume of each cube = (1/4) x (1/4) x (1/4) = 1/64
Total volume = 36 x 1/64 = 9/16
Therefore, both methods give the same volume of 9/16 cubic units.