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.

Solution

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