 Hello and welcome to the session. Let us discuss the following question. It says the diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas. Now we know that earth and moon are in the shape of sphere. So we need to know the formula for the surface area of sphere. It is 4 pi r square where r is the radius of the sphere. So this is the key idea. Let us now move on to the solution. The diameter of earth be d and we are given that the diameter of moon is one fourth of the diameter of the earth. That is diameter of moon is one fourth of d that is d by 4. We know that radius is half of the diameter. So the radius of the diameter that is d by 2 of the diameter of moon that is half of d by 4 which is equal to d by 8. Now we need to find the surface areas of moon and earth. So we first find surface area of moon. The formula for surface area of sphere is 4 pi r square where r is the radius. So the surface area of moon is 4 pi here r is d by 8. So 4 pi into d by 8 square. So it is equal to 4 pi into d square upon 64. Now we find the surface area of the radius of earth is d by 2. So the surface area of earth is 4 pi into d by 2 square which is equal to 4 pi into d square by 4. Now we find the ratio of the surface areas of moon is to the surface area of equal to 4 pi into d square upon 64 upon into d square upon 4. 4 pi gets cancelled with 4 pi and we have d square upon 64 upon d square upon 4 which is equal to d square upon 64 into 4 upon d square. d square gets cancelled with d square. We have 4 upon 64 which is equal to 1 upon 16. So the ratio is 1 is to 16. Hence the ratio of surface areas of earth and moon is 1 is to 16. So that's all for the session. Goodbye and take care.