Question

Arionna claims that since there are 3 feet in a yard, there are 9 cubic feet in a cubic yard. Which statement about her claim is true?

a.)Arionna is correct because there are 3 feet across the length of a cubic yard and 3 feet across the depth of a cubic yard. 3 times 3 = 9
b.)Arionna is correct because there are 3 feet in a yard and there are 3 dimensions in a cubic yard: length, depth, and height. 3 times 3 = 9
c.)Arionna is incorrect. There are only 3 cubic feet in a cubic yard because there are 3 feet in a yard, and the proportion will remain constant.
d.) Arionna is incorrect. There are 27 cubic feet in a cubic yard because a cubic yard is a prism with dimensions 3 ft Times 3 ft Times 3 ft. A prism with those dimensions will take 27 cubes to fill it if each cube is a unit cube of 1 ft.

Answer 1

d.) Arionna is incorrect. There are 27 cubic feet in a cubic yard because a cubic yard is a prism with dimensions 3 ft times 3 ft times 3 ft. A prism with those dimensions will take 27 cubes to fill it, if each cube is a unit cube of 1 ft³.

Explanation:

There are (3 ft)(3 ft) = 9 ft² in one square yard. To find the volume of a cubic yard, you need to multiply that by 3 ft again: (9 ft²)(3 ft) = 27 ft³.

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Additional comment

For many problems involving units, I like to keep the units with the numbers. That helps ensure the math is done correctly. In this problem, simply multiplying ft by ft gives ft^2, not ft^3, so you know right away that you haven't computed volume correctly.