Use the image to answer the question.

Question

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.

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

17.9 in.
17.9 in.

13.9 in.
13.9 in.

11.3 in.
11.3 in.

8.0 in.

Answer 1

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

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

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

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

Now, we calculate \( \sqrt{3} \):

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

Now multiply that by 8:

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

Rounding this result to the nearest tenth:

\[ d \approx 13.9 , \text{inches} \]

Therefore, the length of the diagonal of the cube \( d \) is:

13.9 in.