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

13.9 in.
13.9 in.
17.9 in.
17.9 in.
11.3 in.
11.3 in.
8.0 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, which is given by:

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

where \( a \) is the length of an edge of the cube.

Given that \( a = 8 \) in, we can substitute this value into the formula:

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

Next, we can approximate \( \sqrt{3} \). The approximate value of \( \sqrt{3} \) is about \( 1.732 \).

So, we can calculate:

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

Now, rounding \( 13.856 \) to the nearest tenth, we get:

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

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