Quadrilateral 16603

Calculate the volume of a regular quadrilateral pyramid, which has the size of the base edge a = 8 cm and the length of the side edge h = 9 cm.

Final Answer:

V =  149.3333 cm³

Step-by-step explanation:

$$\begin{gathered} a=8\text{cm} \\ s=9\text{cm} \\ S=a^2=8^2=64{\text{cm}}^2 \\ u=\sqrt{2}\cdot a=\sqrt{2}\cdot 8=8\sqrt{2}\text{cm}\doteq 11.3137\text{cm} \\ h=\sqrt{s^2-(u/2{)}^2}=\sqrt{9^2-(11.3137/2{)}^2}=7\text{cm} \\ V=\frac{1}{3}\cdot S\cdot h=\frac{1}{3}\cdot 64\cdot 7=149.3333{\text{cm}}^3 \end{gathered}$$

Try another example