The volume of the cone in terms of π is:
A. 392π in³
The radius of the cone i.e. r is: 7 in.
and the slant height of the cone i.e. l=y=25 in.
and let h=x be the height of the cone.
Now, using the Pythagorean Theorem we have:
[tex]l^2=r^2+h^2\\\\i.e.\\\\h^2=l^2-r^2\\\\i.e.\\\\h^2=(25)^2-7^2\\\\i.e.\\\\h^2=625-49\\\\i.e.\\\\h^2=576\\\\i.e.\\\\h=\sqrt{576}\\\\i.e.\\\\h=24[/tex]
Hence, we get:
[tex]h=x=25\ in.[/tex]
Now, the volume of the cone is given by:
[tex]Volume=\dfrac{1}{3}\pi r^2h\\\\i.e.\\\\Volume=\dfrac{1}{3}\times\pi\times (7)^2\times 24\\\\i.e.\\\\Volume=392\pi\ in^3[/tex]
Hence, the answer is: Option: A
