 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says a solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of the water left in the cylinder if the radius of the cylinder is 60 cm and its height is 180 cm. Now we know that volume of cone is equal to 1 by 3 pi r square h where r is the radius h is the height volume of hemisphere is equal to where r is the radius of the hemisphere volume of cylinder is equal to r square h where r is the radius h is the height of the cylinder. So this is a key idea behind our question. We will take the help of this key idea to solve the above question. So let's start the solution. It is given in the question that a solid consisting of a right circular cone of height 120 cm and this is the height of the cone 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm. The volume of this solid is equal to volume of cone plus volume of hemisphere. Now this solid is placed in a cylinder full of water when this solid is placed in a cylinder full of water it displaces some water and the water it displaces is equal to its own volume. We have to find the volume of water left in the cylinder when this solid is placed in a cylinder. Volume of water left in the cylinder will be equal to the volume of water in the cylinder minus volume of this solid the volume of this solid. Now we are given the height of the cone is equal to 120 cm let us convert it into meters. So this is equal to 120 upon 100 meter because 1 meter is equal to 100 cm and this is again equal to 1.2 meter and radius of cone is equal to 60 cm and this is equal to 60 upon 100 meter and this is equal to 0.6 meter. Now the radius of hemisphere is equal to 60 cm and this is equal to 60 upon 100 meter which is again equal to 0.6 meter. Therefore volume of this solid is equal to volume of cone. Volume of according to our key idea volume of cone is equal to 1 by 3 pi r square h. Volume of hemisphere which is 2 by 3 pi r cube let us take 1 by 3 pi r square common so we have volume of solid is equal to 1 by 3 pi r square into h plus 2 r and this is again equal to 1 by 3 pi. Now r is 0.6 meter which is 1.2 meter plus 0.6 meter this is again equal to 1 by 3 pi into 0.36 into 1.2 plus 1.2 meter cube and this is equal to 1 by 3 pi into 0.36 into 2.4 meter cube and the volume of the solid is equal to 0.8 into 0.36 per the cylinder is 60 centimeter which is equal to 0.6 meter and height of the cylinder is 180 centimeter which is equal to 1.8 meter. Therefore volume of water in the cylinder is equal to pi r square h because this is a formula for volume of cylinder and this is equal to pi into 0.6 square into 1.8 meter cube and this is equal to 1.8 into 0.36 pi meter cube. Now volume of the solid is 0.8 into 0.36 pi meter cube and volume of water in the cylinder is 1.8 into 0.36 pi meter cube hence volume of water left in the cylinder is equal to volume of water in the cylinder minus volume of solid this is equal to 1.8 into 0.36 pi meter cube minus 0.8 into 0.36 pi meter cube let us take 0.5 common volume of water left in the cylinder is equal to 0.36 pi into 1.8 minus 0.8 meter cube and this is again equal to 0.36 into take pi is equal to 22 upon 7 into 1 meter cube and this is equal to 7.92 upon 7 meter cube and this is again equal to 1.131 meter cube approximately. Hence the answer for the above question is that volume of water left in the cylinder is 1.131 meter cube approximately. I hope the solution is clear to you. Bye and take care.