 Hello and welcome to the session. The given question says, a solid is in the form of a right circular cylinder with hemispherical ends. The total height of the solid is 58 centimeters and diameter of the cylinder is 28 centimeters. Find the total surface of the solid. Let's start with the solution and let this be a right circular cylinder with two hemispherical ends such that the total height of the solid is 58 centimeters and the diameter of cylinder is 28 centimeters. So we are given the total height cylindrical with hemispherical ends is equal to 58 centimeters. Also we are given the diameter of the cylinder is equal to 28 centimeters. So this implies that radius of the cylinder, let us denote it by small r is equal to diameter divided by 2, that is 28 divided by 2 which is equal to 14 centimeters. Now from this figure you can see that the radius of the cylinder is equal to the radius of the hemisphere, right? So radius of cylinder is equal to the radius of hemisphere and this is also equal to small r is equal to 14 centimeters. Now let us find the height of the cylinder which is Po. So Po is equal to qA which is 58 centimeters minus OA and qP plus we have height of the cylinder denoting it by small h is equal to qA minus of qP plus OA and this is further equal to the total height of the cylinder is 58 centimeters minus qP is the radius of the hemisphere. So this is equal to 14 plus 14 and this is equal to 58 minus 28 which is equal to 30 centimeters. So the height of the cylinder is 30 centimeters. Now we have to find the total surface area of the solid and this is equal to the curved surface area of the cylinder plus two times the curved surface area of the hemisphere. This is further equal to curved surface area of the cylinder is given by 2 pi Rh plus two times the curved surface area of hemisphere which is equal to 2 pi r square. So this on further simplifying equals to taking 2 pi r common here we are left with h plus and here we are left with 2 times of r. Now substituting the values we have 2 into we have to use pi as 22 by 7 into rs the radius of the cylinder or the hemisphere which are both equal equals to 14 into h which is 30 plus 2 times of 14. This is further equal to 7 2s of 14. So 22 into 4 into 30 plus 28 and this is equal to 58 and this is further equal to 22 into 4 into 58 and this is equal to 5104 centimeters square. Hence the answer is the total surface area of this solid is 5104 centimeters square. So this completes the session by intake care.