Find the volume of the right rectangular prism using the cube method. Each cube is 35
inch on each side. What is the volume of the prism? Write your answer as a mixed number.
To find the volume of a rectangular prism using the cube method, we need to count the number of cubes that fit into the prism.
The dimensions of the prism are: length = 7 inches, width = 5 inches, height = 6 inches.
We will start by finding the volume of each layer of cubes. Since each cube is 35 inches on each side, the volume of each cube is 35*35*35 = 42,875 cubic inches.
Next, we will find the number of cubes that fit in each layer:
- For the base layer: 7 cubes fit along the length and 5 cubes fit along the width. Therefore, there are a total of 7*5 = 35 cubes in the base layer.
- For each subsequent layer, the number of cubes will remain the same since the length and width of the prism don't change.
Finally, we will multiply the volume of each cube by the number of cubes in each layer to find the total volume of the prism:
Total volume = 42,875 cubic inches * 6 layers = 257,250 cubic inches
To write the answer as a mixed number, we need to convert the total volume to cubic feet, as 1 cubic foot = 1728 cubic inches.
257,250 / 1728 = 148 whole feet with a remainder of 426 cubic inches.
Therefore, the volume of the prism is 148 426/1728 cubic feet.