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:

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

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