 Hello students, let's work out the following problem. It says the radius of the base and the height of the solid circular cylinder are in the ratio 2s to 3 and its volume is 1617 cubic centimetre. Find the total surface area. So let's now move on to the solution. We have given that the radius of the base and the height of the cylinder are in the ratio 2s to 3. So, let the radius of base of the cylinder be 2x centimetre and the height of the cylinder be 3x centimetre. Now, we are given that the volume of cylinder is 1617 cubic centimetre and we know that the volume of the cylinder is given by the formula pi r square h and this is very important to write the formula. From this, we have pi r square h is equal to this. So, now pi is 22 by 7 into r is 2x centimetre into h which is 3x centimetre and this is equal to 1617. Now, simply find this, go further, we have 2x square into 3x is equal to 1617 into 7 upon 22 and this again implies 2x square is 4x square 2x to the power 2 is 4x square into 3x is equal to 1617 into 7 upon 22. Now, 4 into 3 is 12 and x cube into x is x to the power 2 into x is x cube. So, this becomes 12x cube is equal to 1617 into 7 upon 22 and this implies x cube is equal to 1617 into 7 upon 22 into 12. Now, this implies x cube is equal to 1617 into 7 upon 22 can be written as 2 into 11 for 12 can be written as 4 into 3. Now, dividing 1617 by 11 gives us 147 and dividing 147 by 3 gives us 49. So, we have x cube is equal to 49 into 7 upon 2 into 4 can be written as 2 into 2. So, this implies x cube is equal to 7 into 7 49 is written as 7 into 7 upon 2 into 2 into 2. So, this implies x cube is equal to 7 by 22 the power 3. Now, taking cube root on both sides, we have x is equal to 7 by 2. Now, we have radius of base is equal to 2x centimeter. So, this is 2 into 7 by 2 centimeter which is equal to 7 centimeter and the height of the cylinder is 3x centimeter. So, it becomes 21 by 2 centimeter. Now, we have to find the total surface area of the cylinder. Total surface area of the cylinder is given by the formula 2 pi r h plus 2 pi r square and you must remember to write the formula. Let us now substitute the values of pi r and h in the formula. So, we have 2 into 22 by 7 into 7 radius is 7 centimeter into h which is 21 by 2 centimeter plus 2 pi r square 7 into 7. Simplifying this 22 into 21 plus 22 into 14 again this is equal to taking 22 common we have 22 into 21 plus 4 this is 22 into its 14 or 4. So, it is 22 into 35 which is equal to 770. And you have to write the unit of the total surface area which is centimeter square not centimeter cube. Hence, the total surface area of the cylinder is 770 centimeter square. So, this completes the question and the session. Bye for now. Take care. Have a good day.