 Hello and welcome to the session. Let us discuss the following question. It says, 27 solid iron spheres each of radius r and surface area s are melted to form a sphere with surface area s' and the radius r' of the new sphere ratio of s and s' Let us now move on to the solution. We are given that 27 solid iron spheres of radius r are melted to form a sphere of radius r' so the volume of small sphere of a small sphere 4 by 3 pi r' This is the formula for the volume of the sphere 4 by 3 pi r' where r is the radius of the sphere Now this is the volume of small sphere So the volume of 27 small spheres is equal to 27 into 4 by 3 into pi r' We are given that the radius of the new sphere is r' So the volume of large sphere is equal to 4 by 3 pi r' because the radius of the larger sphere is r' So the volume of the large sphere is 4 by 3 pi r' Now the large sphere we have obtained by melting 27 small spheres that is 27 small spheres together form a large sphere that means volume of 27 small spheres is equal to the volume of one large sphere So if this is 1 and this is 2 So this implies 1 is equal to 2 So this implies 27 into 4 by 3 pi r' So this implies 27 into 4 by 3 pi r' So this implies 27 into 4 by 3 pi r' Pi r' is equal to 4 by 3 pi r' This implies r' is equal to 27 into 4 by 3 pi r' upon 4 by 3 pi Now 4 by 3 pi gets cancelled with 4 by 3 pi and this implies r' q is equal to 27 r' Now taking the cube root we have r' is equal to 3r Now in the second part we have to find the ratio of s and s' s is the surface area of 27 solid iron spheres and s' is the surface area of one large sphere So let us now discuss the second part Now the surface area a small sphere pi r' where r is the radius of the small sphere that is s' r' and the surface area pi r' q the radius of the large sphere is r' So the surface area of large sphere is 4 pi r' but r' is 3r So it is 4 pi into 3 and the large sphere is s' So s' is equal to 9 into 3 is 9 and this is 9 into 4 pi r' Now the ratio s' is equal to the surface area of small sphere which is 4 pi r' is to surface area of larger sphere which is 9 into 4 pi r' which is equal to 4 pi r' upon 9 into 4 pi r' 4 pi r' gets cancelled with 4 pi r' and this is 1 upon 9 So the ratio is 1 is to 9 Hence the radius of the new sphere is 3r s' is 1 is to 9 That completes the question Bye for now, take care, have a good day