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.

13.9 in.
13.9 in.

11.3 in.

Answer 1

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

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

In your case, the edge length \( a \) is 8 inches. Plugging this value into the formula:

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

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

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

Now substitute back into the equation:

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

Rounding \( 13.856 \) to the nearest tenth gives:

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

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