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
OK
I forgot to add that the radius of the circle in the first diagram is s
You should not reason on volumes but on areas
You can find by saying that the area of the circle (without cut sector) is equal to the area of the lateral side of the cone (formula is )
Since area of the curved surface of a cylinder is A=2*Pi*r*h Would it make sense seeing the relationship between the volume of the two to take that and multiply it by 1/3? If not(which I am guessing is the case considering that it does not correspond with the formula you submitted), do you know how to derive the formula?