 Hello and welcome to the session. My name is Asha and I shall be helping you with the following question which says the diameter of the moon is approximately one fourth the diameter of the earth. What fraction of the volume of the earth is the volume of the moon? So first let us learn the formula to find the volume of a sphere. This is equal to 4 upon 3 pi r cube where r is the radius of this sphere. So with the help of this formula we are going to solve the above problem. So this is our key idea. Let us now begin with the solution and here we are given that diameter of the moon is approximately one fourth of the diameter of earth. So let the diameter of earth is equal to d units. So this implies the diameter of moon is equal to one fourth the diameter of earth that is 3 upon 4 units. This implies that radius of earth is equal to d upon 2 units. Since find the radius from diameter we divide the diameter by 2 and similarly radius of moon is equal to d divided by 4 divided by 2 units that is equal to d upon 8 units. Now we have to find what fraction of the volume of the earth is the volume of the moon? That is we have to find the ratio of volume of earth on volume of moon. Now both moon and earth are of spherical shape So to find the volume of earth and moon we shall be using the formula to calculate the volume of a sphere. So we have 4 upon 3 into pi into r cube where r is the radius. So to find the volume of earth its radius is d upon 2 units. So we have d upon 2 whole cube on in the denominator we have 4 upon 3 into pi into and the radius of moon is d upon 8 units. So we have d upon 8 whole cube. So we have 4 upon 3 into pi into d cube upon 8 divided by 4 upon 3 into pi into d cube upon 8 cube is 512. Now 4 upon 3 cancels out with 4 upon 3 pi with pi d cube for d cube and we have 512 upon 8 and this is further equal to 64. Thus we have volume of earth divided by volume of moon is equal to 64 upon 1 or we can say that in other words volume of moon cross multiplying is equal to 1 upon 64 times the volume of earth that is 64th portion of the volume of earth is the volume of moon. Hence our answer is 1 upon 64th fraction of the volume of earth is the volume of moon. So this completes the session. Bye and take care.