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?
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\times3 = 9 ).
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\times3 = 9 ).
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.
arionna is incorrect. there are 27 cubic feet in a cubic yard because a cubic yard is a prism with dimensions ( 3 ft\times3 ft\times3 ft ). a prism with those dimensions will take 27 cubes to fill it if each cube is a unit cube of 1 ft.

Explanation:

Step1: Recall the volume formula for a cube

The volume \(V\) of a cube is given by \(V = s\times s\times s=s^{3}\), where \(s\) is the side - length of the cube.

Step2: Convert the side - length of a cubic yard to feet

Since \(1\) yard \( = 3\) feet, for a cubic yard with side - length \(s = 1\) yard \(=3\) feet.

Step3: Calculate the volume of the cubic yard in cubic feet

Using the volume formula \(V=(3\space ft)\times(3\space ft)\times(3\space ft)=3^{3}\space ft^{3}=27\space ft^{3}\)

Answer:

Arionna is incorrect. There are 27 cubic feet in a cubic yard because a cubic yard is a prism with dimensions \(3\space ft\times3\space ft\times3\space ft\). A prism with those dimensions will take 27 cubes to fill it if each cube is a unit cube of \(1\space ft\).