 Hello and welcome to the session. My name is Rasha and I shall be helping you with the following problem which says the students of a Vidyalaya were asked to participate in a competition for making and decorating pen holders in the shape of a cylinder with a base. Using cardboard, each pen holder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition? So let's now start with the solution. And here we are given that shape of a pen holder is of a cylinder with a base of radius Let us denoted by small r so this is equal to 3 cm and also we are given height of cylinder or height of the pen holder is equal to 10.5 cm and let us denoted by h. Now we are required to find how much cardboard is to be bought for 35 such competitors that one competitor has to make one pen holder. So first let us find the area of one pen holder. Now the pen holder is in the shape of a cylinder with base. So we have curved surface area or the lateral surface area area of base Now curved surface area of a cylinder is 2 pi r h where r is the radius of the base and h is the height of the cylinder. So here pen holder is in the shape of a cylinder so we have used the formula to calculate the curved surface area of a cylinder plus now base of a cylinder is a circle so we have pi r square. The scan further written as taking pi r common we have 2 h plus r. So let us denote this by equation number 1. Now substituting the value of r and h to get the area of one pen holder we have pi is 22 upon 7 into 3 into 2 times of 10.5 plus 3 thus is further equal to 22 upon 7 into 3 into 24 which is further equal to 1584 upon 7. Now since area is in square units and here the radius and the height are given in centimetres so area is centimetres square. Now we have to find area of 35 pen holders since there are 35 competitors so area of 35 pen holders is equal to 1584 upon 7 into 35 centimetres square 7 fights the 35 so this further gives 7,920 centimetres square hence our answer is the cardboard require by the 35 competitors to make such pen holders of radius 3 centimetres and height 10.5 centimetres 7,920 centimetres square so this completes the session. Bye and take care.