Angle of diagonal

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.

Result

V =  2449.49 cm3

Solution:

a=10 cm A=60∘→ rad=60∘⋅ π180 =60∘⋅ 3.1415926180 =1.0472=π/3  u1=2⋅ a=2⋅ 10≐10 2 cm≐14.1421 cm tan⁡A=h/u1  h=u1⋅ tan⁡(A)=14.1421⋅ tan⁡(1.0472)≐10 6 cm≐24.4949 cm  V=a2⋅ h=102⋅ 24.4949≐1000 6≐2449.4897≐2449.49 cm3a=10 \ \text{cm} \ \\ A=60 ^\circ \rightarrow\ \text{rad}=60 ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ =60 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ =1.0472=π/3 \ \\ \ \\ u_{ 1 }=\sqrt{ 2 } \cdot \ a=\sqrt{ 2 } \cdot \ 10 \doteq 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) \doteq 10 \ \sqrt{ 6 } \ \text{cm} \doteq 24.4949 \ \text{cm} \ \\ \ \\ V=a^2 \cdot \ h=10^2 \cdot \ 24.4949 \doteq 1000 \ \sqrt{ 6 } \doteq 2449.4897 \doteq 2449.49 \ \text{cm}^3

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