Question
What is the length of a diagonal of a cube with a side length of 6 inches?
Length of a diagonal of the face:
6 squared + 6 squared = c squared. 36 + 36 = c squared. 72 = c squared. StartRoot 72 EndRoot = c.
Use the diagonal of the face of the cube and the side length of the cube to find the length of the diagonal of the cube. Round to the nearest tenth of an inch.
The diagonal through the interior of the cube is about
inches.
Length of a diagonal of the face:
6 squared + 6 squared = c squared. 36 + 36 = c squared. 72 = c squared. StartRoot 72 EndRoot = c.
Use the diagonal of the face of the cube and the side length of the cube to find the length of the diagonal of the cube. Round to the nearest tenth of an inch.
The diagonal through the interior of the cube is about
inches.
Answers
Answered by
GPT-4o mini
To find the length of the diagonal of a cube, we can use the 3D Pythagorean theorem. The formula for the diagonal \(d\) of a cube with side length \(s\) is given by:
\[
d = \sqrt{s^2 + s^2 + s^2} = \sqrt{3s^2} = s\sqrt{3}
\]
For a cube with a side length of 6 inches, we can substitute \(s = 6\) into the formula:
\[
d = 6\sqrt{3}
\]
Next, we can calculate \(6\sqrt{3}\). The approximate value of \(\sqrt{3} \approx 1.732\), so:
\[
d \approx 6 \times 1.732 = 10.392
\]
Now, rounding to the nearest tenth of an inch:
\[
d \approx 10.4
\]
Therefore, the length of the diagonal of the cube is approximately **10.4 inches**.
\[
d = \sqrt{s^2 + s^2 + s^2} = \sqrt{3s^2} = s\sqrt{3}
\]
For a cube with a side length of 6 inches, we can substitute \(s = 6\) into the formula:
\[
d = 6\sqrt{3}
\]
Next, we can calculate \(6\sqrt{3}\). The approximate value of \(\sqrt{3} \approx 1.732\), so:
\[
d \approx 6 \times 1.732 = 10.392
\]
Now, rounding to the nearest tenth of an inch:
\[
d \approx 10.4
\]
Therefore, the length of the diagonal of the cube is approximately **10.4 inches**.