Angle of diagonal

The angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.

Correct answer:

V =  2449.4897 cm³

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ A=60°\to \text{rad}=60°\cdot \frac{\pi }{180}=60°\cdot \frac{3.1415926}{180}=1.0472=\pi /3 \\ {u}_1=\sqrt{2}\cdot a=\sqrt{2}\cdot 10=10\sqrt{2}\text{cm}\doteq 14.1421\text{cm} \\ \tan A=h/u_1 \\ h=u_1\cdot \tan (A)=14.1421\cdot \tan 1.0472=10\sqrt{6}\text{cm}\doteq 24.4949\text{cm} \\ V=a^2\cdot h=10^2\cdot 24.4949=1000\sqrt{6}=2449.4897{\text{cm}}^3 \end{gathered}$$

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