The length, width, and height of a cube are all labeled a.
A cube has an edge length, a
, that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers.
(1 point)
Responses
the diagonal of one of the cube’s faces
the diagonal of one of the cube’s faces
the volume of the cube
the volume of the cube
the area of one of the cube’s faces
the area of one of the cube’s faces
the surface area of the cube
the surface area of the cube
1 answer
The measurement that will require the use of irrational numbers is:
the diagonal of one of the cube’s faces.
To explain: The diagonal of a face of the cube can be calculated using the Pythagorean theorem. If the edge length of the cube is \( a \), the diagonal \( d \) of a face would be calculated as \( d = \sqrt{a^2 + a^2} = \sqrt{2a^2} = a\sqrt{2} \). Since \( \sqrt{2} \) is an irrational number, this means that the diagonal will also be an irrational number if \( a \) is a rational number.
