Question

Belle wants to build a sandbox in the shape of a rectangular prism. She needs the volume of her sandbox to be 18 cubic feet and the height of her sandbox to be a fraction of 1 over 2 of a foot.

Give two possible sets of dimensions, in feet, for the base of Belle’s sandbox. Justify your answer.

a) The answer does not provide dimensions or justification.
b) Two sets of dimensions are provided without justification.
c) Two sets of dimensions are provided with justification.
d) One set of dimensions is provided with justification.

Answer 1

Two possible sets of dimensions for the base of Belle's sandbox with justification.

Step-by-step explanation:

Two possible sets of dimensions for the base of Belle's sandbox are:

1. Dimensions: 3 feet by 3 feet, 1/2 foot high
2. Justification:
3. The volume formula for a rectangular prism is
4. Volume = Length x Width x Height
5. . So, in this case, the volume would be 3 x 3 x 1/2 = 9/2 = 4.5 cubic feet, which is greater than 18 cubic feet. Therefore, this set of dimensions does not satisfy the requirement of 18 cubic feet.
6. Dimensions: 2 feet by 9 feet, 1/2 foot high
7. Justification:
8. The volume would be 2 x 9 x 1/2 = 9 cubic feet, which is equal to the required volume of 18 cubic feet. Hence, this set of dimensions satisfies the requirement of 18 cubic feet.