Question

Hilda plans to display in a clear cube the needle Betsy Ross used to sew the first American flag. The needle will fit exactly as the diagonal of the cube.

If the side length of the clear cube is StartRoot 3 EndRoot inches, and the diagonal of a face of the cube is StartRoot 6 EndRoot inches, what is the length of the needle?
StartRoot 6 EndRoot inches
3 inches
3 StartRoot 2 EndRoot inches
6 inches

Answer 1

To find the length of the needle, we need to determine the length of the space diagonal of the cube. The diagonal \(d\) of a cube with side length \(s\) can be calculated using the formula:

\[
d = s\sqrt{3}
\]

Given that the side length \(s\) of the cube is \(\sqrt{3}\) inches, we can substitute this value into the formula:

\[
d = \sqrt{3} \sqrt{3}
\]
\[
d = \sqrt{3 \cdot 3} = \sqrt{9} = 3 \text{ inches}
\]

Therefore, the length of the needle is:

\[
\boxed{3} \text{ inches}
\]