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

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

13.9 in.
13.9 in.

17.9 in.
17.9 in.

11.3 in.
11.3 in.

8.0 in.
8.0 in.

GPT-4o mini · Answer

To find the length of the diagonal $ d $ of the cube, we can use the formula for the space diagonal of a cube, which is given by: $$ d = a\sqrt{3} $$ Here, $ a $ is the length of an edge of the cube. Given that $ a = 8 $ inches, we can calculate $ d $: $$ d = 8\sqrt{3} $$ Now, we need to compute $ \sqrt{3} $. The approximate value of $ \sqrt{3} $ is about 1.732. Therefore, $$ d \approx 8 \times 1.732 \approx 13.856 $$ Rounding this to the nearest tenth, we have: $$ d \approx 13.9 \text{ in.} $$ Thus, the length of the diagonal of the cube is $ \boxed{13.9} \text{ in.} $