Question

A rectangular prism is 2 inches by 4 inches by 6 inches.

Kimaya says, “It takes more 2/5-inch cubes to fill the prism than 1/5-inch cubes.”

Do you agree with Kimaya? Explain or show your reasoning.

Answer 1

No, I do not agree with Kimaya, and heres why.

Simple Explanation: 2/5 in. cubes are more than 1/5 in. cubes, so 1/5 in. cubes would take 2x more to fill than 2/5 in.

Complex Explanation: 2 in. x 4 in. x 6 in. is 48 cubic in. and to fill 48 cubic in. using 2/5 in. per cube, it would be 120. as for 1/5 in., to fill 48 cubic in. with that would be 240. Easier way to think of it is that 2/5 in. cubes are already 120 and 1/5 would be doubling that so all you gotta do is multipy 120 x 2 since filling it with 1/5 would be 2x the amount than 2/5.

Hope this helped :D

Answer 2

No, I do not agree with Kimaya. The volume of the rectangular prism is 2 inches x 4 inches x 6 inches = 48 cubic inches. To fill the rectangular prism with 2/5-inch cubes, you would need 48 cubic inches / (2/5) cubic inches per cube = 120 cubes. To fill the rectangular prism with 1/5-inch cubes, you would need 48 cubic inches / (1/5) cubic inches per cube = 240 cubes.

So, it takes less 2/5-inch cubes to fill the prism than 1/5-inch cubes.

Another way to think of it is that the larger the cubes, the less number of cubes you need to fill the same volume, as the cubes are larger in size.