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