 Hello and welcome to the session. Let's discuss the following question. It says a toy is in the form of a cone of radius 3.5 centimeter Mounted on a hemisphere of the same radius the total height of the toy is 15.5 centimeter find the total surface area of the toy So let's now move on to the solution We are given that a cone is mounted on a hemisphere Having radius 3.5 centimeter and the total height of the toy is 15.5 centimeter right and We have to find the surface area of this toy now the radius of the cone is 3.5 centimeter Let's denote it by art and radius of Hemisphere is also are that is 3.5 centimeter Now the total height of the toy is equal to 15.5 centimeter now If the total height is 15.5 centimeter and to find the height of the cone What we'll do is we'll subtract The radius of this sphere hemisphere from the total height since this is the radius of the hemisphere It is 3.5 centimeter Right and the total height of the toy is 15.5 centimeter. So height of the cone Let's denote it by edge will be 15.5 minus 3.5 centimeter and It is equal to 12 centimeter and we have to find the Surface area of this toy so the surface area of the toy Would be equal to the curved surface area of the cone plus This surface area of hemisphere That is we add the surface area of the two now The curved surface area of the cone is pi rl now its surface area of the toy is a so a is pi rl plus Surface area of the hemisphere which is 2 pi r square Now here l is the slant height of the cone that is this height Now we see that it forms a o b forms the right angle triangle and to find this slant height We can apply the Pythagoras theorem is equal to square root of perpendicular plus perpendicular square plus wave square that is 12 square plus 3.5 square That is equal to square root of 144 plus 12.25 That is equal to square root of 156.25 For l is equal to 12.5 centimeter so the slant height is 12.5 centimeter now The surface area a is equal to pi rl R that is the radius is 3.5 into l l is 12.5 centimeter Plus the surface area of the hemisphere which is 2 pi r square That is 2 into pi into 3.5 square taking 3.5 into pi common we have 12.5 plus 2 into 3.5 This implies a is equal to 3.5 pi is 22 by 7 So this is 12.5 plus 2 into 3.5 is 7.0 that is 7 so this implies a is equal to 3.5 into 22 by 7 into 19.5 and this implies a is equal to 214.5 centimeter square So the surface area of the toy is 214.5 centimeter square So this completes the question and the session why for now take care and have a good day