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?

Correct result:

V =  2449.4897 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∘=u1⋅ tan⁡60∘ =14.1421⋅ tan⁡60∘ =14.1421⋅ 1.732051=24.4949  V=S1⋅ h=100⋅ 24.4949=2449.4897 cm3

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