 Hello and welcome to the session. Let's work out the following problem. It says a toy is in the form of Cone mounted on a hemisphere of radius 3.5 centimeter. The total height of the toy is 15.5 centimeter find the total surface area of the toy. So let's now start the solution We are given that a toy is in the form of Cone mounted on a hemisphere the radius of the hemisphere is 3.5 centimeter and the total height of the toy is 15.5 centimeter now since 3.5 centimeter is the radius of the hemisphere and cone is mounted on the hemisphere So radius of cone will be same as radius of hemisphere Which is equal to 3.5 centimeter and we are given that The total height of the toy is 15.5 centimeter now this much is the radius of the Hemisphere so this height is the height of the cone the vertical height is equal to 15.5 minus 3.5 centimeter that is 12 centimeter Now you also need to find the slant height of the cone. This is L if this is A This is O and this is B and the slant height of cone that is AB square or AB is equal to under the root OA square Plus OB square now OA square is 12 square and OB is The radius that is 3.5 now again this is under the root 144 plus 3.5 square 3.5 can be written as 7 by 2 square This is equal to under the root 144 plus 49 by 2 taking LCM and solving we have 625 upon 4 2 square is 4 so this is Square root of 625 is 25 and square root of 4 is 2 so the slant height is 25 upon 2 So AB is 25 by 2 centimeter now the total surface area of the toy is equal to the surface area of cone plus surface area of Hemisphere now The surface area of the cone is given by the formula pi RL where R is the radius L is the slant height and The surface area of the hemisphere is given by the formula 2 pi R square so 25 by 2 is L and This is R So let's now substitute the values of RL and pi in the formula first of all take pi R common So we have L plus 2 R Pi is 22 by 7 R is 3.5 which is written as 7 by 2 L is 25 by 2 plus 2 R R is 7 by 2 Now 7 gets cancelled with 7 2 into 11 is 22 now we have 11 into 25 by 2 plus 7 is 11 into 25 plus 14 by 2 11 into 39 by 2 11 into 39 is 429 upon 2 429 divided by 2 is 214.5 So the total surface area of the toy is 21 point 214.5 centimeters square the total surface area of toy is equal to 214.5 centimeters square so this completes the question and the session life and our take care have a good day