 Hello and welcome to the session. Let's work out the following problem. It says a sector of a circle of radius 12 centimeter has the angle 120 degrees. It is rolled to form a cone. Find the height of the cone. So let's now move on to the solution. We have a sector of circle of radius 12 centimeter and angle 120 degrees. It is rolled to form a cone right. So the slant height of the cone will be the radius of the sector of the circle right and length of arc of the sector of the circle will be the circular base of the cone right. So we first find the circumference of the circular base of the cone that is we first find the length of the arc. So the length of arc of sector of circle is given by the formula pi r into theta upon 180 degrees. Now where theta is 120 degrees and r is 12 centimeter. So length of arc will be equal to pi into 12 into 120 upon 180 degrees. 0 gets cancelled with 0. 3 into 4 is 12. 3 into 6 is 18 and 6 into 2 is 12. So this is equal to 4 into 2 into pi that is 8 pi. Now the circumference of the circular base of cone is equal to the length of arc that is equal to 8 pi. Now we know that the circumference of circle is given by the formula 2 pi r right. So 2 pi r is equal to 8 pi. So this implies r is equal to 8 pi upon 2 pi. This r is the radius of base of the cone. So this implies radius of the base of cone is equal to 8 pi by 2 pi that is 4 pi. So we have radius of the base as 4 pi. Now we have to find the height of the cone. So this we can find out by using the Pythagoras theorem. So this is the right triangle. So the height of cone is given by the formula l square minus r square. Now here l is the slant height of cone which is equal to the radius of sector of circle and it is 12 centimetre and where r is the radius of base of the cone which is equal to 4 pi. So h is equal to under the root 12 square minus 4 pi square. Now since radius of base of the cone is 8 pi by 2 pi the radius of base will be 4 because i gets cancelled with pi. So here also we will be having 4 only. So that here we have 4 square. So this is 12 square is 144 minus 16. So this is equal to under the root 128 which is equal to 11.31 centimetre. So the height of the cone is equal to 11.31 centimetre. So this completes the question and the session. Bye for now. Take care. Have a good day.