 Hello and welcome to the session. Let's work out the following question. It says a vessel is in the form of hollow hemisphere Mounted by a hollow cylinder. The diameter of the hemisphere is 14 centimeter and the total height of the vessel is 13 centimeter Find the surface in a surface area of the vessel. So here we are given a hollow hemisphere mounted by a hollow cylinder and the diameter of the hemisphere is 14 centimeter and The total height of the vessel is 13 centimeter and we have to find the inner surface area of the vessel So the diameter of the hemisphere is 14 centimeter and the total height is 13 centimeter So this total height is 13 centimeter now We have to find the inner surface area of this vessel Now since the diameter is 14 centimeter. So radius would be 7 centimeter and the radius of The cylinder will be same as the radius of The hemisphere since it is mounted on the hemisphere, right? and The height of the cylinder would be the total height minus This radius of the hemisphere. So total height is 13 centimeter and Radius of the hemisphere is 7 centimeter. So the height of the cylinder that is this height This height would be 13 minus 7 that is 6 centimeter right So let's now move on to the solution now the diameter of Hemisphere equal to 14 centimeter Therefore radius of Hemisphere will be 7 centimeter Let's denote it by R and Radius of Hemisphere will be same as radius of the cylinder now the height of the cylinder will be 13 minus 7 that is 6 centimeter Let's denote it by H. So H is 6 centimeter now the Inner surface area of the vessel is equal to the surface area of Hemisphere the surface area of the cylindrical part now if a is the Surface area of the vessel then this implies a is equal to surface area of the hemisphere which is 2 pi r square and Surface area of the cylinder is given by 2 pi r H. Let's now substitute the values of pi r and H in this so we have a is equal to taking 2 pi r common So we have 2 pi r into r plus H now pi is 22 by 7 Radius is 7 centimeter Height is 6 centimeter This is again equal to 2 into 22 into 13 So this is equal to 572 and the unit of the surface area is centimeter square Hence the required answer is 572 centimeters square So this completes the question and the session by for now take care. Have a good day