a cube measures 6 cm on each side. how long is the diagonal that connects two opposite corners of the cube? give an exact answer. 6 cm 6 cm 6 cm the diagonal that connects two opposite corners of the cube is (type an exact answer, using radicals as needed )

Question

Accepted Answer

# Explanation:
## Step1: Find the diagonal of the base
Use the Pythagorean theorem $d_{base}^2 = 6^2+6^2$.
$$
\begin{align*}
d_{base}^2&=36 + 36\
d_{base}^2&=72\
d_{base}&=\sqrt{72}=6\sqrt{2}
\end{align*}
$$
## Step2: Find the space - diagonal
Use the Pythagorean theorem again with the height of the cube ($h = 6$) and the base - diagonal ($d_{base}=6\sqrt{2}$). Let the space - diagonal be $d$. Then $d^2=(6\sqrt{2})^2+6^2$.
$$
\begin{align*}
d^2&=72 + 36\
d^2&=108\
d&=\sqrt{108}=6\sqrt{3}
\end{align*}
$$

# Answer:
$6\sqrt{3}\text{ cm}$

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QUESTION IMAGE

Question

Explanation:

Step1: Find the diagonal of the base

Step2: Find the space - diagonal

Answer: