Right pyramid

A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.

Correct answer:

V =  28.2213 cm³

Step-by-step explanation:

$$\begin{gathered} a=4\text{ cm } \\ s=6\text{ cm } \\ {d}^2=a^2+a^2 \\ {d}^2=2a^2 \\ d=\sqrt{2}\cdot a=\sqrt{2}\cdot 4=4\sqrt{2}\text{ cm}\doteq 5.6569\text{ cm } \\ {s}^2=(d\mathrm{/}2{)}^2+h^2 \\ h=\sqrt{s^2-(d\mathrm{/}2{)}^2}=\sqrt{6^2-(5.6569\mathrm{/}2{)}^2}=2\sqrt{7}\text{ cm}\doteq 5.2915\text{ cm } \\ V={\displaystyle \frac{1}{3}}\cdot a^2\cdot h={\displaystyle \frac{1}{3}}\cdot 4^2\cdot 5.2915=28.2213{\text{cm}}^3 \end{gathered}$$

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