we know that
The volume of the shaded portion of the composite figure is equal to the volume of a rectangular pyramid minus the volume of a cone
so
Step \(1\)
Find the volume of a cone
volume of the cone is equal to
\(Vc=\frac{1}{3}* \pi* r^{2}*h\)
where
r is the radius of the cone
h is the height of the cone
in this problem
\(r=4.5\ units\\ h=12\ units\)
Substitute in the formula above
\(Vc=\frac{1}{3} \pi*4.5^{2}*12\)
\(Vc=81\pi \ units^{3}\)
Step \(2\)
Find the volume of a rectangular pyramid
Volume of a rectangular pyramid is equal to
\(Vp=\frac{1}{3}*B*h\)
where
B is the area of the base
h is the height of the pyramid
in this problem
\(B=10*15=150\ units^{2} \\ h=12\ units\)
Substitute in the formula above
\(Vp=\frac{1}{3}*150*12=600\ units^{3}\)
Step \(3\)
Find the volume of the shaded portion of the composite figure
\(Vp-Vc=(600-81\pi)\ units ^{3}\)
therefore
the answer is
Find the volume of the shaded portion of the composite figure is
\((600-81\pi)\ units ^{3}\)
