Answer:
[tex]V=400\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a pyramid is equal to
[tex]V=\frac{1}{3}BH[/tex]
where
B is the area of the square base
H is the height of the pyramid
Find the area of the square base B
[tex]B=b^{2}[/tex]
[tex]b=10\ cm[/tex]
[tex]B=10^{2}=100\ cm^{2}[/tex]
Find the height H of the pyramid
Applying the Pythagoras Theorem
[tex]l^{2}=H^{2}+(b/2)^{2}[/tex]
we have
[tex]b=10\ cm[/tex]
[tex]l=13\ cm[/tex]
substitute
[tex]13^{2}=H^{2}+(10/2)^{2}[/tex]
[tex]169=H^{2}+25[/tex]
[tex]H^{2}=169-25[/tex]
[tex]H^{2}=144[/tex]
[tex]H=12\ cm[/tex]
Find the volume
[tex]V=\frac{1}{3}(100)(12)[/tex]
[tex]V=400\ cm^{3}[/tex]
