An illustration shows a cube with parts labeled. The front, right, and top faces are visible. The left, back, and bottom faces are not visible, but their positions are indicated by a dotted line. The edges at the bottom front, bottom right, and back right side are all labeled a and represent length, width, and height. A dotted line extends diagonally from the front top left vertex to the bottom right back vertex and is labeled d.

Question

The length of the edge of the cube, a
, is 8 in. Find the length of the diagonal of the cube, d
. Round the answer to the nearest tenth.

(1 point)
Responses

8.0 in.
8.0 in.

17.9 in.
17.9 in.

11.3 in.
11.3 in.

13.9 in.

Answer 1

To find the length of the diagonal of the cube, we can use the formula for the space diagonal \(d\) of a cube with edge length \(a\):

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

Given that the length of the edge of the cube \(a\) is 8 inches, we can substitute this value into the formula:

\[ d = 8\sqrt{3} \]

Now, calculating \(8\sqrt{3}\):

\[ \sqrt{3} \approx 1.732 \]

So,

\[ d \approx 8 \times 1.732 \approx 13.856 \]

Rounding this to the nearest tenth gives:

\[ d \approx 13.9 \text{ in.} \]

Thus, the length of the diagonal of the cube is 13.9 in.