 Hello and welcome to the session. Today I will help you with the following question. The question says diameter of cylinder A is 7 cm and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can we suggest whose volume is greater, verify it by finding the volume of both the cylinders, check whether the cylinder with greater volume also has greater surface area. Let's recall the formula for the volume of cylinder which is equal to pi r square h and surface area of cylinder is equal to 2 pi r multiplied by r plus h, where r is the radius of base of cylinder and h is the height of cylinder. This is the key idea for this question. Now let's move on to the solution. These are the two cylinders given to us cylinder A and cylinder B, the diameter of cylinder A is 7 cm and the height of cylinder A is 14 cm, likewise diameter for cylinder B is 14 cm and its height is 7 cm. We already know that the volume of cylinder is equal to pi r square h. Now if we compare the cylinder A and cylinder B we see that cylinder A has lesser diameter than cylinder B. As you can see that the diameter of cylinder A is 7 cm and diameter of cylinder B is 14 cm and the height of cylinder A is greater but just twice the height of cylinder B. As you can see height of cylinder A is 14 cm and height of cylinder B is 7 cm. As you can see in the formula for the volume of a cylinder we need square of the radius and the height of the cylinder is multiplied just once and also cylinder B has radius double the cylinder A so we say cylinder B will have more volume than cylinder A the radius of cylinder B is more than the radius of cylinder A. Now to verify this we will find the volume of both the cylinders separately. First let's consider the cylinder A the diameter for this cylinder is given to be 7 cm so we have radius r is equal to 3.5 cm also height h is given to be equal to 14 cm we know that the volume is equal to pi r square h now we shall substitute the value for pi r and h so we have this is equal to now the value for pi is 22 upon 7 multiplied by the value for r is 3.5 the whole square multiplied by h which is 14 we know that 7 2 times is 14 so this is equal to 22 multiplied by 3.5 multiplied by 3.5 multiplied by 2 which is further equal to 539 cm cube so we have volume of cylinder A is equal to 539 cm cube now let's consider the cylinder B the diameter for cylinder B is equal to 14 cm so we have radius r is equal to 7 cm also height h is equal to 7 cm we know that the volume is equal to pi r square h now we shall substitute the values for pi r and h so this becomes equal to now the value for pi is 22 upon 7 multiplied by r is 7 so 7 square multiplied by height h is 7 this 7 gets cancelled with this 7 and we are left with 22 multiplied by 7 multiplied by 7 which is equal to 1078 cm cube so we get the volume of cylinder B is equal to 1078 cm cube so finally we have volume of cylinder A equal to 539 cm cube and volume of cylinder B is equal to 1078 cm cube thus we say that cylinder B has greater volume now we shall find the surface area of both the cylinders we know that the surface area of cylinder is equal to 2 pi r multiplied by r plus h surface area of cylinder A is equal to we shall substitute the values for r and h in this formula so we have 2 multiplied by pi that is 22 upon 7 multiplied by r and r for cylinder A is 3.5 centimeters which is further multiplied by r that is 3.5 plus h for cylinder A is equal to 14 centimeters this is equal to 2 multiplied by 22 upon 7 multiplied by 3.5 multiplied by now 14 plus 3.5 is 17.5 7.5 times is 3.5 so this is equal to 2 multiplied by 22 multiplied by 0.5 multiplied by 17.5 and that is equal to 385 centimeters square so we get surface area of cylinder A is equal to 385 centimeters square then again we shall find the surface area of cylinder B and this is equal to 2 pi r multiplied by r plus h now we shall substitute the values for pi r and h that is we have 2 multiplied by now the value for pi is 22 upon 7 multiplied by r which is equal to now for cylinder B the radius r is equal to 7 centimeters so this is multiplied by 7 which is indeed multiplied by now r is 7 plus now the height of cylinder B is 7 centimeters so we write here 7 and this becomes equal to 2 multiplied by 22 upon 7 multiplied by 7 multiplied by now 7 plus 7 is 14 then again we have 7 2 times is 14 this becomes equal to 2 multiplied by 22 multiplied by 7 multiplied by 2 which is equal to 616 centimeters square thus we have surface area of cylinder B is equal to 616 centimeters square surface area of cylinder A is 385 centimeters square and surface area of cylinder B is 616 centimeters square thus we say that cylinder B has greater surface area hence our final answer is volume of cylinder B is greater and surface area of cylinder B is greater so hope you enjoyed the session have a good day