Find the volume of the right rectangular prism packed with 12 cubes. Each cube has an edge length of 12 inch.
(1 point)
Responses:
5 cubic inches
18 cubic inches
32 cubic inches
12 cubic inches
The correct response is not provided.
To find the volume of the right rectangular prism packed with 12 cubes, we first need to find the dimensions of the rectangular prism. Since each cube has an edge length of 12 inches, the length of the rectangular prism will be 12 times some integer, the width will be 12 times some other integer, and the height will be 12 times yet another integer.
We can see that the only way to pack 12 cubes into the rectangular prism is to have dimensions of 24 inches by 12 inches by 6 inches. Therefore, the volume of the rectangular prism is:
24 inches × 12 inches × 6 inches = 1,728 cubic inches
So, the correct response is not provided.
Unless I am not reading the question correctly,
each of the cubes has a volume of 12^3 inches^3
or 1728 cubic inches
but we are told there are 12 of these, so the total volume
= 12*1728 or 20736 cubic inches
You are correct, my apologies for the mistake. The volume of one cube is indeed 1728 cubic inches (12 inches x 12 inches x 12 inches), and since there are 12 cubes, the total volume of the right rectangular prism is:
12 cubes x 1728 cubic inches/cube = 20,736 cubic inches
Thank you for pointing out the error in my previous response.
To find the volume of the right rectangular prism packed with cubes, we need to multiply the number of cubes by the volume of each cube.
In this case, there are 12 cubes and each cube has an edge length of 12 inches. The formula to find the volume of a cube is:
Volume = edge length x edge length x edge length
So, for each cube, the volume would be:
Volume = 12 inches x 12 inches x 12 inches
Simplifying this gives us:
Volume = 1,728 cubic inches
Since there are 12 cubes packed in the prism, we need to multiply the volume of one cube by 12:
Volume of prism = 1,728 cubic inches x 12
Calculating this gives us:
Volume of prism = 20,736 cubic inches
Therefore, the correct answer is 20,736 cubic inches.