 Hello and welcome to the session. In this session we discussed the following question which says a Gulab Jamun when ready for eating contains sugar syrup of about 30% of its volume. Find approximately how much syrup would be found in 45 such Gulab Jamuns, each shaped like a cylinder with 2 hemispherical ends. If the complete length of each of them is 5 cm and its diameter is 2.8 cm. We know that the volume of a cylinder is equal to pi r square h where this r is the radius of the base of the cylinder and h is the height of the cylinder. Then we also know that the volume of the hemisphere is given as 2 by 3 pi r2 where again this r is the radius of the hemisphere. This is the key idea for this question. Now let's move on to the solution. Consider this Gulab Jamun. It is shaped like a cylinder with 2 hemispherical ends. We take r to be equal to radius of the cylinder which is also equal to radius of hemispherical end. We have this r is equal to diameter of the cylinder upon 2. Now we have that the diameter of the cylinder is 2.8 cm so 2.8 upon 2 would be equal to 1.4 cm. Thus we have got the radius of the cylinder and radius of the hemispherical end as 1.4 cm. Now we take h to be the height of the cylinder which would be equal to the complete length of the Gulab Jamun minus 2 times the radius of the hemispherical end. So this would be equal to 5 that is the complete length of the Gulab Jamun minus 2 into 1.4 cm. That is 5 minus 2.8 cm. Thus we get height of the cylinder h is equal to 2.2 cm. The next we need to find the volume of one Gulab Jamun. This would be equal to the volume of the cylindrical portion of the Gulab Jamun that is this portion plus 2 times the volume of hemispherical end. So this is equal to now we know that volume of cylinder is equal to pi r square h. So this is equal to pi r square h plus 2 into volume of the hemisphere that is 2 by 3 pi r cube. So this becomes equal to pi r square into h plus 4 upon 3 r. Now we substitute the values for pi r and h. We take pi to be equal to 22 upon 7 into r square that is 1.4 square into h that is 2.2 plus 4 upon 3 into r that is 1.4 cm cube. So this is further equal to 22 into 1.4 into 0.2 into 2.2 plus 1.867 cm cube. So we have this is equal to 6.16 into 4.067 cm cube which further is equal to 25.05 cm cube approximately. So we get volume of 1 Gulab Jamun is equal to 25.05 cm cube approximately. Next we find the sugar syrup contained in a ready Gulab Jamun is equal to 30% of the volume as given in the question. So this would be equal to 30 upon 100 into volume of 1 Gulab Jamun which is 25.05 cm cube. This gives us 7.515 cm cube approximately is the sugar syrup contained in a ready Gulab Jamun. We need to find the sugar syrup contained in 45 Gulab Jamuns. So we write sugar syrup contained in 45 Gulab Jamuns is equal to 45 into 7.515 cm cube. Now this would be equal to 338.17 cm cube approximately is the sugar syrup contained in 45 Gulab Jamuns. Thus our final answer is 338.17 cm cube approximately syrup would be found in 45 such Gulab Jamuns. So this completes the session. Hope you have understood the solution for this question.