Final answer:
To find the difference in volume of the two cube-shaped storage units, we compute the volume for each using the formula V = s³ and then subtract the smaller volume from the larger. The correct difference is approximately 237.375 cubic feet, which does not match any of the options provided, indicating a possible error in the options or question.
Step-by-step explanation:
The student is tasked with finding the difference in the volume of two cube-shaped storage units. The side length of the larger cube is 8 feet, and the side length of the smaller cube is 6.5 feet. By using the volume formula for a cube, which is V = s³, where s is the side length, we can calculate the volume of each cube.
- Volume of the larger cube: V = 8³ = 8 * 8 * 8 = 512 cubic feet
- Volume of the smaller cube: V = 6.5³ = 6.5 * 6.5 * 6.5 ≈ 274.625 cubic feet
Next, we find the difference by subtracting the smaller volume from the larger volume:
Difference in volume = 512 cubic feet - 274.625 cubic feet ≈ 237.375 cubic feet
However, the closest answer from the options provided is Option B: 270.25 cubic feet, which suggests there may be an error in the options, or a typo in the question as none of the provided options match the calculated volume difference. If this is an exact calculation, the closest accurate answer is not listed among the options provided.