 Hello and welcome to the session, let's discuss the following question. It says a hemispherical bowl of internal diameter 30 centimeter contains some liquid. This liquid is to be filled into cylindrical shaped bottles each of diameter 5 centimeter and height 6 centimeter find the number of bottles necessary to empty the bowl. So let's now move on to the solution. We are given a hemispherical bowl which has diameter 30 centimeter and in this bowl we have some liquid and this liquid is to be filled in some number of bottles each of diameter 5 centimeter and height 6 centimeter. Now volume of this hemispherical bowl will be equal to the volume of all these cylindrical shaped bottles that is volume of this hemispherical bowl is equal to the volumes of the sums of these cylindrical bottles right. So we have to find the number of bottles so let there be n number of bottles. So the volume of hemispherical bowl is equal to the volume of n number of cylindrical bottles. Now the radius of the bowl is equal to 30 by 2 centimeter that is 15 centimeter since 30 centimeter is the diameter and we know that radius is half of the diameter so it is 15 centimeter let this be capital R. Now the volume of the bowl is equal to 2 pi r square as we know that the volume of hemisphere is equal to 2 pi r square where r is the radius so you must write this formula. Now r is 15 so we have volume of hemispherical bowl is 2 into pi into r cube here also it is 15 cube. Now we know that the volume of cylinder is given by the formula pi r square h where r is the radius and h is the height of the cylinder. So now the volume of n number of bottles will be equal to n into volume of one bottle since each bottle has the same radius and the diameter so volume of n number of bottles will be equal to n into volume of one bottle right. Now n into volume of one bottle now the radius say r1 of bottle is 5 by 2 centimeter so r1 is 5 by 2 centimeter and the height is 6 centimeters so the volume is n into pi into r square that is 5 by 2 square into 6 so this is the volume of n number of bottles now volume of n number of bottles is equal to the volume of hemispherical bowl let's name this as a and b and let's name this as 1 so equating a and b we have pi into 15 cube is equal to n into pi into 5 by 2 square into 6 right. So now pi gets cancel on both sides and we have n is equal to 2 into 15 cube that is 15 into 15 into 15 upon 5 by 2 square that is 5 by 2 into 5 by 2 into 6 and here we have in the formula 2 by 3 pi r cube so here also we'll be having 2 by 3 and here we'll have 2 by 3 now 3 into 5 is 15 and 5 gets cancelled with 5 then 5 into 3 is 15 and 3 gets cancelled with 6 and we have this is equal to 2 into 15 by 2 that's not by 2 2 by 15 upon 1 by 2 so this is equal to 2 into 15 into 2 that is 60 so the number of bottles is equal to 60 so this completes the question and the session bye for now take care have a good day