 Hello and welcome to the session. I am Deepika here. Let's discuss the question which says in the given figure an Oil funnel made of tin sheet consists of a 10 centimeter long cylindrical portion attached to a first term of a cone. If the total height is 22 centimeter Diameter of the cylindrical portion is 8 centimeter and diameter of the top of the funnel is 18 centimeter Find the area of the tin sheet required to make the funnel now we know that curved surface area of a cylinder is equal to 2 pi r h Where r is the radius of the base of the cylinder and h is the height of the cylinder again curved surface area of a frustum of a cone is equal to pi l r1 plus r2 Where it is equal to under root of h square plus r1 minus r2 whole square where h is the Vertical height of the frustum h is the Vertical height of the frustum is the slant height of the frustum and r1 and r2 are Radiation of two bases of the frustum So this is a key idea behind our question We will take the help of this key idea to solve the above question. So let's start the solution It is given total height of The oil funnel is 22 centimeter Height of the cylindrical portion is 10 centimeter therefore height of the frustum is equal to 22 centimeter minus 10 centimeter and this is equal to 12 centimeter Now it is given diameter of the cylindrical portion is equal to 8 centimeter therefore radius of cylindrical portion is equal to 4 centimeter a cylindrical portion is attached to a frustum of a cone therefore the radius of the base of the frustum is 4 centimeter The diameter of the top of the funnel is 18 centimeter therefore radius of the top of the funnel is equal to 9 centimeter That is the radii r1 of the base of the frustum is equal to 9 centimeter Now we want to find the area of the tin sheet required to make the funnel for this We have to find the curved surface area of the cylindrical portion plus curved surface area of a frustum of a cone Now for the curved surface area of a frustum of a cone We will first find out the slant height of the frustum So l is equal to the root of h square Plus r1 minus r2 Whole square now the vertical height of the frustum is 12 centimeter So l is equal to under root of 12 square plus 9 minus 4 square and this is equal to under root of 144 plus 5 square and which is 25 and this is equal to under root of 169 and this is equal to 13 centimeter hence the slant height is 13 centimeter now the area of the tin sheet required is equal to curve surface area cylindrical portion curve surface area frustum portion This is equal to 2 pi r2 h. This is a curve surface area of cylindrical portion plus Pi l r1 plus r2 and this is equal to 2 into 22 over 7 into r2 is 4 centimeter and height of this cylindrical portion is 10 centimeter plus pi into l l is 13 centimeter and r1 is our 9 centimeter plus 4 centimeter and this is equal to Let us take 22 upon 7 common. So we are left with 80 plus 13 into 13 that is 169 and this is again equal to 22 upon 7 into 249 centimeter square and this is again equal to 5478 upon 7 centimeter square therefore area of the tin sheet required is equal to 782 and 4 by 7 centimeter square Hence the answer for the above question is 782 and 4 by 7 centimeter square. I hope the solution is clear to you. Bye and take care