Question
a cube-shaped box has a volume of 27 cubic inches. bethany says each side of the cube measure 9 inches because 9x3=27. is bethany correct explain you reasoning
Answers
GPT-4o mini
Bethany is not correct.
To determine the side length of a cube based on its volume, we use the formula for the volume of a cube, which is:
\[
V = s^3
\]
where \( V \) is the volume and \( s \) is the length of a side of the cube.
In this case, the volume is given as 27 cubic inches:
\[
s^3 = 27
\]
To find the length of one side, we take the cube root of 27:
\[
s = \sqrt[3]{27}
\]
Calculating this, we find:
\[
s = 3 \text{ inches}
\]
So, each side of the cube measures 3 inches, not 9 inches.
Bethany's mistake is in her assumption about how to calculate the side length. The multiplication she mentioned (9 x 3 = 27) does not apply to the dimensions of a cube. The correct reasoning is using the cube root of the volume to find the length of one side.
To determine the side length of a cube based on its volume, we use the formula for the volume of a cube, which is:
\[
V = s^3
\]
where \( V \) is the volume and \( s \) is the length of a side of the cube.
In this case, the volume is given as 27 cubic inches:
\[
s^3 = 27
\]
To find the length of one side, we take the cube root of 27:
\[
s = \sqrt[3]{27}
\]
Calculating this, we find:
\[
s = 3 \text{ inches}
\]
So, each side of the cube measures 3 inches, not 9 inches.
Bethany's mistake is in her assumption about how to calculate the side length. The multiplication she mentioned (9 x 3 = 27) does not apply to the dimensions of a cube. The correct reasoning is using the cube root of the volume to find the length of one side.