The volume of the cylinder is 12320 cm3 is less than the volume of the sphere. The radius of the sphere is 2.625 times the height of the cylinder. The volume of the cube is 551368 cm3 whose side is 5 cm more than the radius of the cylinder. Find out the lateral surface area of the cylinder.

The volume of the cube is 551368 cm³ . volume of the cube = (side)³ 551368 = (side)³ 82³ = (side)³ Side = 82 cm Side is 5 cm more than the radius of the cylinder. radius of the cylinder = (82-5) = 77 cm    Eq.(i) The volume of the cylinder is 12320 cm³ is less than the volume of the sphere. Let’s assume the radius of cylinder and sphere are ‘rc‘ and ‘rs‘ respectively. Let’s assume the height of the cylinder is ‘h’. (22/7)x(rc)²xh = (4/3)x(22/7)x(rs)³ - 12320 The radius of the sphere is 2.625 times the height of the cylinder. (22/7)x(77)²xh = (4/3)x(22/7)x(2.625h)³ - 12320 [From Eq.(i)] (22/7)x5929xh =  (88/21)x18.0878906h³ - 12320 22x847xh =  75.7968749xh³ - 12320 After solving the above equation, there will be three values of ‘h’. But out of which two are negative which are not possible. So h = 16 (Only possible value of ‘h’.) Lateral surface area of the cylinder = 2x(22/7)x77x16 = 2x22x11x16 = 7744 cm³