 Hello and welcome to the session. In this session we will discuss about surface areas. Let's try and find out the surface areas of some solids like cuboid, cube, cylinders, cones and spheres. First we have the surface area of a cuboid is given by the formula 2 into LB plus BH plus HL where we have L is the length of cuboid, B is the breadth of cuboid and H is the height of cuboid. When we find out the surface area of the cuboid we consider all the six faces of the cuboid. Now when we exclude the area of the top and the bottom faces of the cuboid, the area of the remaining four faces is called the lateral surface area of the cuboid. So next we have lateral surface area of a cuboid is given by the formula 2 into L plus B into H where again L is the length of cuboid, B is the breadth and H is the height of the cuboid. The surface area of the cuboid is sometimes referred as the total surface area. Consider a cuboid of length equal to 5 centimeters, breadth equal to 2 centimeters and the height H equal to 3 centimeters. Now the total surface area or you can say the surface area of this cuboid is given by 2 into LB plus BH plus HL centimeters square. We take the unit of area as the square unit. This is a very important thing that we need to remember. This is equal to 2 into 31 that is 62 centimeters square is the surface area of the cuboid. Next the lateral surface area of the cuboid is given by 2 into L plus B into H that is equal to 42 centimeters square. Next we have surface area or we can say total surface area of a cube its formula is 6 into A square where this A is the edge of the cube and the lateral surface area of a cube is equal to 4 into A square where again A is the edge of the cube. Let's consider a cube of edge equal to 3 centimeters then the surface area of the cube is equal to 6 into A square centimeter square. So this is equal to 54 centimeters square then the lateral surface area of the given cube is equal to 4 into A square that is equal to 36 centimeters square. Next we should consider the formulae for right circular cylinder. First we have the curved surface area of a cylinder here by the word cylinder we mean the right circular cylinder. And this is given by the formula 2 pi R H where we have R is the radius of the base of the cylinder and this H is the height of the cylinder. Then next formula for the total surface area of a right circular cylinder or you can say of a cylinder is given by the formula 2 pi R into R plus H. Consider the cylinder where this H is the height of the cylinder given by 4 centimeters and the base radius or the radius of the base of the cylinder that is R is given by 3 centimeters. So now the curved surface area of this cylinder is given by 2 pi that is 22 upon 7 R H this is equal to 528 upon 7 and which is equal to 75.43 centimeters square. Similarly we can find the total surface area of this cylinder this is equal to 2 pi R into R plus H this is equal to 2 into 22 upon 7 into 3 into 7. So this comes out to be equal to 132 centimeters square. Now let's consider the right circular cone or you can simply say cone it's one and the same thing. First we have the formula for the curved surface area of a cone this is equal to pi R L where we have this R is the base radius of the cone and L is the plant height of the cone. And the formula for the total surface area of the cone or the right circular cone is given by pi R into L plus R. Consider this cone where this H is the height of the cone, R is the base radius of the cone and L is the slant height of the cone. This slant height of the cone that is L is given by square root H square plus R square. Suppose we have height of the cone H equal to 4 centimeters, radius of the base equal to 3 centimeters that is we have R equal to 3 centimeters. So from here we get this slant height L equal to square root 4 square plus 3 square that is equal to square root 25 and thus we get this slant height L equal to 5 centimeters. So now we can easily find out the curved surface area of the cone which is given by pi R L 330 upon 7 and that is equal to 47.14 centimeters square is the curved surface area of the cone. In the same way we can find out the total surface area of this cone equal to pi R into L plus R. This is equal to 528 upon 7 which is further equal to 75.43 centimeters square is the total surface area of the given cone. Next we discuss the formula for the sphere and for the hemisphere. So we have surface area of a sphere is equal to 4 pi R square where this R is the radius of the sphere. Half portion of the sphere is called the hemisphere so the formula for the curved surface area of hemisphere is equal to half of the surface area of the sphere that is 2 pi R square. Where this R is the radius of the sphere of which the hemisphere is a part then we have the total surface area of hemisphere is given by the formula 3 pi R square. Consider this hemisphere with R that is the radius equal to 7 centimeters so the curved surface area of the given hemisphere is equal to 2 pi R square. From here we get the curved surface area of the hemisphere is equal to 308 centimeters square then the total surface area of the given hemisphere is equal to 3 pi R square which is equal to 462 centimeters square. So this completes this session. Hopefully you have understood how we find the surface areas of cuboid, cube, cylinder, cone, hemisphere and sphere.