The graphs show measurements from cubes with different side lengths.Which pairs of variables have a linear relationship? Choose two correct answers.Responsesperimeter of 1 face and area of 1 faceperimeter of 1 face and area of 1 faceside length and volumeside length and volumearea of 1 face and surface areaarea of 1 face and surface areaside length and perimeter of 1 faceside length and perimeter of 1 facesurface area and volume
Question
The graphs show measurements from cubes with different side lengths.Which pairs of variables have a linear relationship? Choose two correct answers.Responsesperimeter of 1 face and area of 1 faceperimeter of 1 face and area of 1 faceside length and volumeside length and volumearea of 1 face and surface areaarea of 1 face and surface areaside length and perimeter of 1 faceside length and perimeter of 1 facesurface area and volume
Solution
The pairs of variables that have a linear relationship are:
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Side length and perimeter of 1 face: This is because the perimeter of a face of a cube is calculated as 4 times the side length. Therefore, if you increase the side length, the perimeter of one face will also increase linearly.
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Area of 1 face and surface area: The surface area of a cube is calculated as 6 times the area of one face. Therefore, if the area of one face increases, the total surface area of the cube will also increase linearly.
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