where,
r is the base radius of the cone
h is the perpendicular height of the cone
In this case,
r = 10.5 / 2= 5.25in
h = 6.75in
[tex]\begin{gathered} \text{Therefore} \\ \text{volume of cone}=\frac{\pi\times5.25^2\times6.75}{3}=194.83in^3 \end{gathered}[/tex]Volume of a ball is given by
[tex]\text{volume of ball =}\frac{4}{3}\times\pi\times r^3[/tex]where r is the radius of the ball
in this case,
[tex]r=\frac{8\frac{1}{2}}{2}=4.25in[/tex]Therefore
[tex]\text{Volume of ball = }\frac{4\times\pi\times4.25^3}{3}=321.56in^3[/tex][tex]\begin{gathered} \text{The difference betw}een\text{ the two volumes=321.56-194.83}=126.73 \\ =126.73in^3 \end{gathered}[/tex]