Answer:
Part a) The volume of the original pyramid is [tex]15\ cm^{3}[/tex]
Part b) The volume of the pyramid increases by [tex]6\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
h is the height of pyramid
Step 1
Find the volume of the original pyramid
the area of the base B is equal to
[tex]B=3^{2}=9\ cm^{2}[/tex]
[tex]h=5\ cm[/tex]
substitute
[tex]V=\frac{1}{3}(9)(5)=15\ cm^{3}[/tex]
Step 2
Find the volume of the new pyramid
[tex]B=9\ cm^{2}[/tex] -------> the area of the base is the same
[tex]h=5+2=7\ cm[/tex] ------> the height increase by [tex]2\ cm[/tex]
substitute
[tex]V=\frac{1}{3}(9)(7)=21\ cm^{3}[/tex]
Subtract the original volume from the new volume
[tex]21\ cm^{3}-15\ cm^{3}=6\ cm^{3}[/tex]
