 Hello and welcome to the session. In this session we will discuss a question which says that a tri is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21 centimeters and its volume is too non free of the volume of the hemisphere, calculate height of the cone and surface area of the toy and use pi is equal to 22 by 7. Now before starting the solution of this question we should know some results. And the first is volume of the hemisphere is 2 by 3 by r2 where r is the radius of the hemisphere. 3. Corrupt surface area of the hemisphere is equal to 2 by r2 where r is the radius of the hemisphere. Thirdly, volume of the cone is equal to 1 by 3 by r2 h where r is the radius of the cone and h is the height of the cone. And the correct surface area of the cone is equal to pi rl where l is the slant height of the cone which is also given by square root of r square plus h square where r is the radius and h is the height of the cone. Now these results will work out as a key idea for solving out this question. And now we will start with the solution. Now it is given that a toy is in the form of the hemisphere surmounted by a white square cone of the same radius at that of the hemisphere. First of the base of the cone is 21 cm. So it is given that the radius of the base of the cone is equal to radius of the hemisphere equal to 21 cm that is equal to 21 cm. So it is given that the volume of the cone is equal to 2. Now this is the formula for the volume of the hemisphere and this is the formula for the volume of cone. Now given volume of the cone into volume of the hemisphere. Now by the formula volume of the cone is 1 by 3 by r square h is equal to 2 by 3 into volume of the hemisphere solving this implies x is equal to 2 into 2 by 3 into r. Now radius value is 21 cm. So putting this value here this implies h is equal to 2 into 2 by 3 into 21 cm. Further this implies h is equal to now here 3 into 7 is 21 so on solving this is equal to 28 cm. Now to find out the slant height of the cone we will use this formula equal to square root of h here here r is 21 cm and h is 28 cm. So this will be equal to square root of 21 square plus 28 square which is further equal to square root of 441 plus 784 which is equal to square root of 1225 which is equal to 35 cm. Now we have to find out the surface area of the toy. Now the surface area of the toy be equal to curve surface area plus area of hemisphere this area of the cone. So putting these values here this will be equal to pi rl plus further equal to taking some common random brackets it will be l. Now putting the values of r here this will be equal to pi which is 22 by 7 into 21 into l that is 3 into r that is 21. Now this is equal to now 7 into 3 is 21 so it will be 22 into 3 into now this is 35 plus 2 into 21 is 42 which is equal to 22 into 3 into 77 which is further equal to 2082 cm square. Therefore is equal to 28 cm this area of the toy is equal to 5000 and 82 cm square. That is the solution of the given question and that is all for this session hope you all have enjoyed the session.