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

11.3 in
11.3 in

8.0 in
8.0 in

17.9 in

1 answer

To find the length of the diagonal of a cube, we can use the formula:

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

Where \( d \) is the length of the cube's diagonal and \( a \) is the length of an edge of the cube.

In this case, the length of the edge \( a = 8 \) inches. We can plug this value into the formula:

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

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

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

Now substituting this value back into the equation:

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

Rounding this to the nearest tenth gives:

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

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