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
17.9 in
17.9 in
8.0 in
8.0 in
11.3 in
11.3 in
13.9 in
(1 point)
Responses
17.9 in
17.9 in
8.0 in
8.0 in
11.3 in
11.3 in
13.9 in
Answers
GPT-4o mini
To find the length of the diagonal of a cube, you can use the formula:
\[
d = a\sqrt{3}
\]
where \( a \) is the length of the edge of the cube.
Given that the length of the edge, \( a = 8 \) in, we can calculate:
\[
d = 8\sqrt{3}
\]
Calculating \( \sqrt{3} \approx 1.732 \):
\[
d \approx 8 \times 1.732 \approx 13.856
\]
Rounding to the nearest tenth, we get:
\[
d \approx 13.9 \text{ in}
\]
So, the length of the diagonal of the cube is approximately **13.9 in**.
\[
d = a\sqrt{3}
\]
where \( a \) is the length of the edge of the cube.
Given that the length of the edge, \( a = 8 \) in, we can calculate:
\[
d = 8\sqrt{3}
\]
Calculating \( \sqrt{3} \approx 1.732 \):
\[
d \approx 8 \times 1.732 \approx 13.856
\]
Rounding to the nearest tenth, we get:
\[
d \approx 13.9 \text{ in}
\]
So, the length of the diagonal of the cube is approximately **13.9 in**.