 Hello and welcome to the session, let's discuss the following question. It says a hemispherical depression is cut out from one face of cubical wooden block such that diameter L of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid. So let's now move on to the solution. We are given a cubical wooden block from which a hemispherical depression is cut out. We have to find the surface area of the remaining solid. Now the hemispherical depression is cut out in such a way that its diameter is equal to the edge of the cube. Now edge of the cube is L and diameter of the hemisphere is also L. Therefore radius of hemisphere would be L by 2. Now we have to find the surface area of the remaining solid. So the surface area of remaining solid would be surface area of cubical block minus area of base of hemisphere plus the curved surface area of the hemisphere. We are subtracting area of base of hemisphere because surface area of cubical block already includes this. So we need to subtract this and since by cutting a hemispherical depression we are getting the curved surface of the hemisphere. So we are adding the curved surface area of the hemisphere. Now this is, if this is denoted by A and this implies A is equal to surface area of cubical block would be 6 into L square as we know that surface area of cube is 6 into side square and it has edge L. So it is 6 L square minus area of the base of the hemisphere. Now base of the hemisphere would be a semi-circle. It would be a circle. So it has area pi r square where r is the radius of the circle. So it would be pi into L by 2 square plus curved surface area of the hemisphere which is 2 pi r square r is the radius. So this implies A is equal to 6 L square minus pi L square by 4 plus 2 pi L square by 4 and this implies A is equal to 6 L square plus pi L square by 4 and this again implies A is equal to 24 L square plus pi L square upon 4. This implies A is equal to taking L square common from the numerator we have L square by 4 into 24 plus pi. Hence the surface area of the remaining solid is L square by 4 into pi plus 24. So this completes the question and the session. Bye for now. Take care. Have a good day.