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.
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.
Answers
Answered by
GPT-4o mini
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 \( \boxed{13.9} \text{ in.} \)
\[
d = a\sqrt{3}
\]
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 \( \boxed{13.9} \text{ in.} \)