Prism diagonal

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

Result

V =  2449.49 cm3

Solution:

a=10 cm A=60 ∘  S1=a2=102=100 cm2 u1=2⋅ a=2⋅ 10≐10 2 cm≐14.1421 cm  tan⁡A=h/u1 h=u1⋅ tan⁡(A∘→ rad)=u1⋅ tan⁡(A∘⋅ π180 )=14.142135623731⋅ tan⁡(60∘⋅ 3.1415926180 )=24.4949  V=S1⋅ h=100⋅ 24.4949≐1000 6≐2449.4897≐2449.49 cm3a=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 \doteq 10 \ \sqrt{ 2 } \ \text{cm} \doteq 14.1421 \ \text{cm} \ \\ \ \\ \tan A=h/u_{1} \ \\ h=u_{1} \cdot \ \tan( A ^\circ \rightarrow\ \text{rad})=u_{1} \cdot \ \tan( A ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=14.142135623731 \cdot \ \tan( 60 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=24.4949 \ \\ \ \\ V=S_{1} \cdot \ h=100 \cdot \ 24.4949 \doteq 1000 \ \sqrt{ 6 } \doteq 2449.4897 \doteq 2449.49 \ \text{cm}^3

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