The question is as follows:

The first diagram shows a circular sector of radius 10 cm and an angle of theta radians (not the angle of the cut out sector). The second diagram shows it formed into a cone of slant height 10 cm. the vertical height, h, of the cone is equal to the radius, r of its base. Find the angle theta in radians.

My reasoning is as follows:

10^2 = 2x^2

x= 7.07

V=1/3Pi 7.07^2*7.07

V=370 cm cubed

My reasoning was as follows the volume obtained would seem to be equal to the area of a volume of a cylinder - the volume of the sector cut out. Have I done something completely wrong?

V= Pi*r^2*h - 1/2 theta r^2 *h