
Volume of a cone
A cone is formed by rolling up a 90 degree sector of a circle having a radius of 8 inches. Find the volume of the cone to the nearest tenth
l is equal to 8. I am having a problem finding the radius and the height. I want to say the lateral area and the base form a 60 degree angle, I am not told this so do not want to assume anything. Help to figure out how to start of where to start would be great thanks.

You can work out the radius, $\displaystyle r$, of the cone from the circumference formed when the sector is folded around. So use the given radius, $\displaystyle R$, and the angle given to work out the length around the edge of the sector and that will be the circumference of the base of the cone.
Then use the Pyathagoras' theorem with R and r to work out the height.