sum of the total surface areas of the cone and hemisphere. Example : The decorative block shown in Fig. . is made of two solids — a cube and a hemisphere.
The base of the block is a cube with edge cm, and the hemisphere fixed on the top has a diameter of . cm. Find the total surface area of the block. (Take = Solution : The total surface area of the cube = × (edge) = × × cm = cm .
Note that the part of the cube where the hemisphere is attached is not included in the surface area. So, the surface area of the block = TSA of cube – base area of hemisphere + CSA of hemisphere = – r + r = ( + r ) cm . . cm = ( + .
Example : A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in Fig. . . The height of the entire rocket is cm, while the height of the conical part is cm.
The base of the conical portion has a diameter of cm, while the base diameter of the cylindrical portion is cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take = . ) Solution : Denote radius of cone by r , slant height of cone by l , height of cone by h , radius of cylinder by r and height of cylinder by h .
Then r = . cm, h = cm, r = . cm, h = – = cm and l = h . = .
cm Here, the conical portion has its circular base resting on the base of the