Respuesta :
Given:
The altitude of a right circular cone = 15
The radius of the base = 8
A cylindrical hole of diameter 4 is drilled through the cone, with its axis along the axis of the cone.
So, the radius of the cylinder = 2
We will find the height of the cylinder using the ratio and proportional
Let the height of the cylinder = h
so,
[tex]\begin{gathered} \frac{h}{15}=\frac{6}{8} \\ \\ h=\frac{6\cdot15}{8}=11.25 \end{gathered}[/tex]So, the height of the cylinder = 11.25
The volume of the solid = the volume of the cone - the volume of the cylinder
The volume of the cone =
[tex]\frac{1}{3}\pi\cdot r^2h=\frac{1}{3}\cdot3.14\cdot8^2\cdot15=1004.8[/tex]The volume of the cylinder =
[tex]\pi\cdot r^2\cdot h=3.14\cdot2^2\cdot11.25=141.3[/tex]So, the volume of the solid =
[tex]1004.8-141.3=863.5[/tex]so, the answer will be: Volume of the solid = 863.5
