 Hello students let's work out the following question it says from a solid cylinder whose height is 2.4 cm and diameter 1.4 cm a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest square centimeters. So let's now move on to the solution we are given a solid cylinder from which a conical cavity is hollowed out having height same as cylinder and the diameter same as cylinder. Now the height of the cylinder let's denote it by r is given to be 2.4 cm and the diameter of cylinder is 1.4 cm therefore radius of cylinder would be half of it that is 1.4 by 2 cm that is equal to 0.7 cm. Now this is the height so let's denote it by h and let's denote the radius by r. Now radius of cone would be same as radius of cylinder and height is also same as the height of the cylinder that is 2.4 cm again this is r and this is h. Now the slant height of the cone is l and we can find out this slant height using Pythagoras theorem because O B forms the right angle triangle so it would be square root of h square plus r square right. Now this is equal to square root of h square that is 2.4 square plus 0.7 square this is equal to 5.76 plus 0.49 that is again equal to square root of 6.25 and it is equal to 2.5 square root of 6.25 is 2.5 so l is 2.5 cm. Now we have to find the total surface area of the remaining solid that is we have to find this surface area of the solid. Now the total surface area of remaining solid let's denote it by capital A would be equal to the curved surface area of the cylinder we know that the curved surface area of the cylinder does not include the circular ends of the cylinder and here we have one circular end left out after cutting the conical cavity so we will add surface area of the base and also when we cut the conical cavity we will get curved surface of the cone so we need to add the curved surface area of the cone so this implies A is equal to curved surface area of the cylinder is 2 pi r h where r is the radius h is the height surface area of the base now surface is circular so its area would be pi r square and the curved surface area of the cone is pi r l right so this implies A is equal to taking pi r common from the whole expression we have 2 h plus r plus l and this implies A is equal to putting the value of pi as 22 by 7 into r which is 0.7 into 2 h h is 2.4 plus r which is 0.7 plus l which is 2.5 now this implies A is equal to 22 by 7 into 7 by 10 into 4.8 plus 0.7 plus 2.5 so this implies A is equal to 2.2 into 4.8 plus 0.7 plus 2.5 is 8.0 or 8 we can say so this implies A is equal to 17.6 the total surface area of remaining solid is 17.6 centimeter square and to the nearest centimeter square would be 18 centimeter square by rounding of this we get it as 18 centimeter square so this is the required answer so this completes the question and the session bye for now take care have a good day.