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