 Hi friends and how are you all doing today. Let us discuss this question. It says a solid cube of site 12 cm is cut into 8 cubes of equal volume. What will be the side of the new cube? Also find the ratio between their surface areas. So here the question says that let this be a solid cube of so measuring 12 cm each. Now this cube has to be divided into 8 cubes of equal volume. So that means the volume of these cubes is obviously smaller than this bigger one we need to find out the side of this cube and then we need to find out the ratio between their surface areas. Before proceeding on let us be well versed with the volume of a cubes formula that is site cube and surface area of a cube is equal to 6 side square. So these are some key ideas for this question. Now after understanding the concept we can easily proceed on with the solution. Let us find out the volume of the big cube that is 12 cube that is further equal to 1728 cm cube. So volume of a small cube will be 1728 cm cube divided by 8 it is equal to 216 cm cube. Also volume of a small cube will be what? It will be side cube isn't it? So the value of side cube is given to us as 216 cm cube that implies we can find out this side by finding out the cube root of 216 cm cube it is 6 cm x 6 cm x 6 cm right that gives us the answer as 6 cm. So this is the side of the new cube the small cube is the new cube also we need to find out the ratio of the surface areas that is 6 x side cube side square that is 12 x 12 for the bigger one 6 x 6 x 6 for the new cube. So after simplifying we get the answer as 4 x 1 that is equal to 4 x 1. So the final answer to the session is first of all 6 cm is the side of the new cube and the ratio of the surface area is 4 x 1. So this completes my session have a good day bye for now.