Find the volume of the right rectangular prism using the cube method Each cube is 1/3 inch on each side. What is the volume of the prism? Provide your answer as a fraction reduced to the lowest terms
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To find the volume of the right rectangular prism using the cube method, you need to determine the number of unit cubes that can fit inside the prism and multiply it by the volume of each cube.
Given that each cube is 1/3 inch on each side, we can calculate the volume of each cube as follows: (1/3) x (1/3) x (1/3) = 1/27 cubic inches.
Now, to find the volume of the right rectangular prism, we need to determine the number of cubes that can fit along each dimension. Let's assume the dimensions of the prism are length, width, and height.
Let's say the length of the prism is L inches, the width is W inches, and the height is H inches.
To find the number of cubes that can fit along the length, we divide L by 1/3: L / (1/3) = L x (3/1) = 3L cubes.
Similarly, the number of cubes that can fit along the width would be 3W cubes and along the height would be 3H cubes.
Therefore, the total number of cubes that can fit inside the prism is (3L) x (3W) x (3H) = 27LWH cubes.
Finally, multiplying the total number of cubes by the volume of each cube (1/27 cubic inches) gives us the volume of the prism:
Volume = Number of cubes x Volume of each cube = 27LWH x 1/27 = LWH cubic inches.
So, the volume of the right rectangular prism is LWH cubic inches.
Please provide the values for length, width, and height so that we can calculate the volume as a fraction reduced to the lowest terms.
To use the cube method, count the number of small cubes needed to fill the rectangular prism.
The length of the prism is 4 times the length of a small cube, so it will require 4 rows of cubes.
The width of the prism is 3 times the width of a small cube, so it will require 3 columns of cubes.
The height of the prism is 6 times the height of a small cube, so it will require 6 layers of cubes.
Thus, the number of small cubes needed to fill the rectangular prism is:
4 x 3 x 6 = 72
Therefore, the volume of the prism is:
72 x (1/3)^3 = 72/27 = 8/3
So the volume of the prism is 8/3 cubic inches, or 2 and 2/3 cubic inches.