Square pyramid

Calculate the pyramid's volume with the side 5cm long and with a square base, side-base has an angle of 60 degrees.

Correct answer:

V =  18.0422 cm³

Step-by-step explanation:

$$\begin{gathered} s=5\text{ cm } \\ A=60^{\circ } \\ \cos (A)=(u\mathrm{/}2)\mathrm{/}s \\ \cos (A)=u\mathrm{/}(2s) \\ u=2\cdot s\cdot \cos (A^{\circ }\to \text{ rad})=2\cdot s\cdot \cos (A^{\circ }\cdot {\displaystyle \frac{\pi }{180}})=2\cdot 5\cdot \cos (60^{\circ }\cdot {\displaystyle \frac{3.1415926}{180}})=5\text{ cm } \\ a=u\mathrm{/}\sqrt{2}=5\mathrm{/}\sqrt{2}\doteq 3.5355\text{ cm } \\ S=a^2=3.5355^2={\displaystyle \frac{25}{2}}=12.5{\text{cm}}^2 \\ h=s\cdot \sin (A^{\circ }\to \text{ rad})=s\cdot \sin (A^{\circ }\cdot {\displaystyle \frac{\pi }{180}})=5\cdot \sin (60^{\circ }\cdot {\displaystyle \frac{3.1415926}{180}})=4.33013\text{ cm } \\ V=S\cdot h\mathrm{/}3=12.5\cdot 4.3301\mathrm{/}3=18.0422{\text{cm}}^3 \end{gathered}$$

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