The volume of the square pyramid
is given by:
[tex]V=\frac{1}{3}Bh[/tex]where:
[tex]B=s^2[/tex]where s is the edge of the base.
In this case s = 12.
Therefore,
[tex]B=12^2=144\text{ in}^2[/tex]h = 10.
[tex]\begin{gathered} V=\frac{1}{3}\times144\times10=480 \\ V=480\text{ in}^3 \end{gathered}[/tex]Hence, the volume of the square based pyramid is given by:
V = 480 in³
Hence, the volume of the pyramid is correct.
The volume of cylinder is given by:
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi\times6.77^2\times10 \\ V\approx1440\text{ in}^3 \end{gathered}[/tex]Therefore, Jude use the wrong formula for computing the volume of the cylinder.
Hence, the correct answer is:
No, he made a mistake in solving for the volume of the cylinder.
