 Hello and welcome to the session. The given question says, the base radius and height of a right circular solid cone are 2 cm and 8 cm respectively. It is melted and recast it into a sphere of diameter 2 cm each. Find the number of spheres so formed. Let's start with the solution. Here we are given a right circular cone whose base radius is 2 cm and also we are given its height is equal to 8 cm. So let us denote the base radius of the right circular cone by small r and height by h. Now it is given that it is melted and recast it into spheres of diameter 2 cm each. We have to find the number of spheres so formed. Suppose this is a cone whose height is 8 cm and base radius is 2 cm and suppose its volume is capital V. Now it is melted and recast it into a number of small spheres each of diameter 2 cm. This is also 2 cm right. Now we have to find the number of spheres so formed. Now the volume of this cone must be equal to the volume of the n number of spheres so formed. Since when a solid is melted and recast it into another solid then the volume of two solids are equal. So first let us find the volume of the right circular cone. It is given by 1 by 3 pi r square h. So on substituting the values we have 1 divided by 3 into pi into r is 2 cm so we have 2 square into h is 8 cm cubed. So this is further equal to 32 pi divided by 3 cm cubed. Now according to the equation we have recast it into small spheres of diameter 2 cm. So we are given diameter of sphere is equal to 2 cm. Therefore its radius is equal to diameter divided by 2 that is 2 divided by 2 which is equal to 1 cm. Now let us find its volume. Volume of a sphere is given by 4 by 3 pi. Let us denote the radius of the sphere by capital R so we have here r cubed. On substituting the values we have 4 divided by 3 pi cm cubed since r is equal to 1 cm. Now let the number of spheres formed from the right circular cone when it is melted and recast it is equal to. So this implies the volume of cone is equal to n times the volume of therefore we have n is equal to volume of cone divided by the volume of spheres. Now let us substitute the values. So here we have 32 divided by 3 pi cm cubed divided by the volume of sphere is 4 divided by 3 pi cm cubed. So this is further equal to 32 divided by 3 pi cancels of the pi into 3 divided by 4. 8 is 32 so n is equal to 8. So the number of spheres formed from the right circular cone are 8. So this completes the session by intake care.