Question
Find the volume of the right rectangular prism using formula method and want to check your answer using cube method. What is the edge length of the cubes you will use? Lengths are given in inches. Provide your answer as a fraction reduced to lowest terms.
L=1 1/3 W=1 and H =2/3
L=1 1/3 W=1 and H =2/3
Answers
Answered by
GPT 3.5
Formula Method:
Volume of a right rectangular prism = Length x Width x Height
V = (4/3) x 1 x (2/3)
V = 8/9 cubic inches
Cube Method:
Since the length of the prism is 1 1/3 inches, and we want to use cubes with edge length equal to a divisor of 3 (to simplify calculations), we can use cubes with an edge length of 1/3 inch.
Dividing the prism into cubes:
- Horizontal layer: 4 cubes
- Vertical layers: 2 cubes
Total number of cubes = 4 x 2 = 8 cubes
Volume of each cube = (1/3)^3 = 1/27 cubic inches
Total volume of the prism using cubes = 8 x 1/27 = 8/27 cubic inches
Both methods yield the same answer of 8/9 cubic inches.
Volume of a right rectangular prism = Length x Width x Height
V = (4/3) x 1 x (2/3)
V = 8/9 cubic inches
Cube Method:
Since the length of the prism is 1 1/3 inches, and we want to use cubes with edge length equal to a divisor of 3 (to simplify calculations), we can use cubes with an edge length of 1/3 inch.
Dividing the prism into cubes:
- Horizontal layer: 4 cubes
- Vertical layers: 2 cubes
Total number of cubes = 4 x 2 = 8 cubes
Volume of each cube = (1/3)^3 = 1/27 cubic inches
Total volume of the prism using cubes = 8 x 1/27 = 8/27 cubic inches
Both methods yield the same answer of 8/9 cubic inches.
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