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
To use the cube method, we count the number of cubes that can fit inside the rectangular prism.
Let the dimensions of the rectangular prism be l, w, and h. We divide each dimension by 1/3 to determine the number of cubes that can fit in each direction:
- The length l can fit \frac{l}{1/3}=3l cubes.
- The width w can fit \frac{w}{1/3}=3w cubes.
- The height h can fit \frac{h}{1/3}=3h cubes.
Therefore, the total number of cubes that can fit inside the rectangular prism is 3l x 3w x 3h = 27lwh.
Each cube has a volume of (1/3)^3 = 1/27 cubic inches. Therefore, the volume of the rectangular prism is:
27lwh x (1/27) = lwh.
So the volume of the right rectangular prism is lwh expressed as a fraction reduced to the lowest terms.
To find the volume of the right rectangular prism using the cube method, we need to count the number of smaller cubes that can fit inside the prism.
Let's say the length, width, and height of the prism are L, W, and H respectively.
First, we need to determine the number of cubes that fit along the length of the prism. Since each cube is 1/3 inch on each side, the number of cubes along the length would be L * (3/1) = 3L.
Next, we determine the number of cubes that fit along the width of the prism. Similarly, it would be W * (3/1) = 3W.
Finally, we determine the number of cubes that fit along the height of the prism. It would be H * (3/1) = 3H.
Multiplying all these values together, we get the total number of cubes that fit inside the prism: 3L * 3W * 3H = 27LWH.
Therefore, the volume of the prism is 27LWH cubic inches.
To find the volume of a right rectangular prism using the cube method, we need to determine how many unit cubes can fit inside the prism.
Given that each cube has a side length of 1/3 inch, we can think of the prism's dimensions as multiples of 1/3 inch.
Let's assume the dimensions of the prism are a, b, and c units in each direction. To find the number of cubes that fit in the prism, we divide each dimension by 1/3:
Number of cubes in the a direction = a / (1/3) = 3a
Number of cubes in the b direction = b / (1/3) = 3b
Number of cubes in the c direction = c / (1/3) = 3c
The total number of cubes is given by multiplying these values:
Total number of cubes = (3a) * (3b) * (3c) = 27abc
Since each cube has a volume of (1/3) * (1/3) * (1/3) = 1/27 cubic units, the volume of the prism is the total number of cubes multiplied by the volume of each cube:
Volume of the prism = (27abc) * (1/27) = abc
Therefore, the volume of the right rectangular prism using the cube method is abc, expressed as a fraction reduced to the lowest terms.