 Hello and welcome to the session. I am Deepika here. Let's discuss the question which says derive a formula for the curved surface area and total surface area of the frustum of a cone given to us in section 13.5 using the symbols as explained. Now in section 13.5 there was the removal of a smaller right circular cone by cutting the given cone by a plane parallel to its base. So let's start the solution. Now in this figure a right circular cone VAB is cut by a plane parallel to its circular base with center O and diameter AB. The portion containing the vertex V is removed. The left round portion ABP-A- is the of the cone VAB. Now the line segment O- joining the centers of two circular bases is the vertical height of the frustum. Therefore O- is equal to VO-VO-. Now the slant height of the frustum ABB-A- is AA- and which is equal to BB-. Let H be the vertical height and L be the slant height and R1 and R2 be the radii of the two circular bases of the frustum ABB-A- such that R1 is greater than R2 that is this is HO- is H and AA- and BB- are the slant heights and this is L. OB is R1 and O-V- is R2 that is O- is equal to H and AA- is equal to VB- is is equal to L and OB is equal to R1 and O-B- is equal to R2. Let the height of the cone VAB-BH1 and its slant height be L1 so VO- is equal to H1 and VA- is equal to VB- is equal to L1. Now VA- is equal to VA-AA- and this is equal to L1-L and VO- is equal to VO-OO- and this is equal to H1- H. Now triangle VOA is similar to triangle VO-A- because VO- is equal to angle A-VO common angle VOA is equal to angle VO-A- is equal to 90 degree so this implies VO upon VO- is equal to OA upon OA- is equal to VA upon VA- and this implies H1 upon H1- H is equal to R1 upon R2 and this is equal to L1 upon L1- L and this implies H1- H upon H1 is equal to R2 upon R1 is equal to L1- L upon L1 and this implies 1- H upon H1 is equal to R2 upon R1 and this is equal to 1- L upon L1 and this implies H upon H1 is equal to 1- R2 upon R1 and L upon L1 is equal to 1- R2 upon R1 and this implies H upon H1 is equal to R1- R2 upon R1 and L upon L1 is equal to R1- R2 upon R1 and this implies H is equal to H1 into R1- R2 upon R1 and L is equal to L1 into R1- R2 upon R1 and this implies H1 is equal to H R1 upon R1- R2 and L1 is equal to L R1 upon R1- R2 therefore height of the cone VA-B dash is equal to H1- H and this is equal to H R1 over R1- R2- H and this is again equal to H R2 upon R1- R2 and slant height of the cone VA-B dash is equal to L1- L which is equal to L R1 upon R1- R2- L and this is equal to L R2 upon R1- R2 let S be the curve surface area of the frustum of a cone therefore S is equal to curve surface area of cone VA-B minus curve surface area of cone VA-B dash so this implies S is equal to pi R1 L1 minus pi R2 L1 minus L because we know that the curve surface area of a cone is pi RL and this implies S is equal to pi R1 now L1 is R L R1 upon R1- R2 minus pi R2 into L R2 upon R1- R2 this implies S is equal to take pi N common R1 square minus R2 square upon R2- R2 R1 minus R2 and this implies S is equal to pi L R1 plus R2 because R1 square minus R2 square is R1 plus R2 into R1 minus R2 thus curve surface area of a frustum of a cone is equal to pi L R1 plus R2 now the total surface area of a frustum of a cone is equal to curve surface area plus area of the two circular basis and this is equal to pi N R1 plus R2 plus pi R1 square plus pi R2 square and this is equal to pi L R1 plus R2 plus pi R1 square plus R2 square hence the answer for the above question is curve surface area is equal to pi L R1 plus R2 and total surface area is equal to pi L R1 plus R2 plus pi R1 square plus R2 square I hope the solution is clear to you. Bye and take care.