 Hello and welcome to the session. I am Deepika here. Let's discuss the question which sees. A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy. Use pi is equal to 22 over 7. Now we know that the curved surface area of cone is equal to pi rn where r is the radius and l is the slant height which is given by under root of r square plus h square and here h is the height of the cone. Again, curved surface area of hemisphere is equal to 2 pi r square where r is the radius of hemisphere. So this is the 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. According to the given question, a toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. We have to find the total surface area of the toy. So let a, b, c, b, a cone mounted on a hemisphere of common base radius 7 cm. So according to our key idea, the curved surface area of hemisphere is equal to 2 into 22 over 7 because here we are given use pi is equal to 22 over 7 into r square. Now here r is 7 cm. So the curved surface area of hemisphere is equal to 2 into 22 over 7 into 7 into 7 cm square. Now since the total height of the toy is 31 cm, therefore the height of the conical portion is equal to 31 minus 7 cm and this is equal to 24 cm. So this height that is a o is 24 cm. Now we will find out the slant height of the cone. Now according to our key idea, the slant height of the cone which is given by L is equal to under root of r square plus h square and this is equal to under root of 7 square plus 24 square cm and this is again equal to under root of 49 plus 576 cm and this is again equal to under root of 625 cm which is equal to 25 cm. Hence the curved surface area of cone is equal to pi RL which is again equal to 22 over 7 into 7 into 25 cm square. Now the total surface area the toy is equal to curved surface area of the hemisphere plus the curved surface area of cone. Now the curved surface area of hemisphere is equal to 2 into 22 over 7 into 7 into 7 cm square and curved surface area of cone is equal to 22 over 7 into 7 into 25 cm square. So on substituting these values we have the total surface area of the toy is equal to 2 into 22 over 7 into 7 into 7 plus 22 over 7 into 7 into 25 cm square and this is again equal to 22 over 7 into 7 into 14 plus 25 cm square and this is again equal to 22 into 39 cm square and this is equal to 858 cm square. Hence the total surface area of the toy which is in the form of a cone mounted on a hemisphere is equal to 858 cm square. So this is the answer for the above question. This completes our session. I hope the solution is clear to you. Bye and have a nice day.