Prism diagonal

The body diagonal of a regular square prism has an angle of 60 degrees with the base, and the edge length is 10 cm. What is the volume of the prism?

Correct answer:

V =  2449.4897 cm³

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ A=60{}^{\circ } \\ {S}_1=a^2=10^2=100{\text{cm}}^2 \\ {u}_1=\sqrt{2}\cdot a=\sqrt{2}\cdot 10=10\sqrt{2}\text{cm}\doteq 14.1421\text{cm} \\ \tan A=h/u_1 \\ h=u_1\cdot \tan A=u_1\cdot \tan 60°=14.1421\cdot \tan 60°=14.1421\cdot 1.732051=24.4949\text{cm} \\ V=S_1\cdot h=100\cdot 24.4949=1000\sqrt{6}=2449.4897{\text{cm}}^3 \end{gathered}$$

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