 Hello and welcome to the session. In this session we discuss a question which says that Emma is playing by the beach. She takes a cylindrical bucket and fills it with wet sand. She turns it upside down to dump the sand in the ground and sand takes the shape of the bucket which is a cylinder with radius 4 inches and height 14 inches. She now takes a mold in the form of a cone with radius 3 inches and height 7 inches and does the same. Now she dumps the sand in the shape of the cone on top of the cylinder she formed before. Find the volume of sand used by Emma. Now before starting the solution of this question you should know some results. First of all the volume of the cylinder is equal to iR square H where is the radius of cylinder and H is the height of cylinder and volume of cone is equal to 1.3 iR square H where is the radius of cone and H is the height of cone. Now these results will welcome you as a key idea for solving out the given question. Now let us start with the solution of the given question. Now in the given question we want to find the volume of sand that Emma has collected on the ground in the form of a cylinder and a cone molded over it. Now let radius of cylinder is equal to iR1 height of cylinder VH1 radius of cone H2. Now given radius of cylinder that is iR1 is equal to 4 inches height of cylinder that is H1 is equal to 15 inches radius of cone that is R2 is equal to 3 inches and height of cone that is H2 is equal to 7 inches. Now using the result which is given to us in the key idea volume of cylinder is equal to iR1 square H1 as iR1 is the radius of cylinder and H1 is the height of cylinder. So given the values of I1 and H1 we have volume of cylinder is equal to now pi is equal to 22 by 7 into I2 square that is 4 into 4 into H1 which is 14. So this is equal to now 7 into 2 is 14 and this is equal to 22 into 32 which is equal to 104 cubic inches. Now volume of cone is equal to 1 by 3 H2 the radius of cone and H2 is the height of cone. Now given the values of R2 and H2 where 1 by 3 into pi which is 22 by 7 into R2 square that is 3 into 3 into H2 which is 7. Now 7 into 1 is 7 and 3 into 1 is 3. So this is equal to now the value of sand used by Emma is equal to volume of sand used to form the cylinder plus volume of sand used to form the cone. Now here volume of cylinder which is 705 cubic inches is the volume of sand used to form the cylinder and volume of cone which is 66 cubic inches is the volume of sand used to form the cone. The volume of sand used by Emma is equal to volume of sand used to form the cylinder, volume of sand used to form the cone 704 cubic inches so this is equal to 3 cubic inches. So the volume of sand used by Emma is equal to 770 cubic inches and this is the solution of the given question. Let's talk about the session hope you all have enjoyed the session.