The sum of the area of two ends of a right circular cylinder is equal to 1 3 of its curved surface. Find ratio of the height and diameter of the cylinder.

Let the height of the right circular cylinder be H and the diameter of the right circular cylinder be R . Radius of the right circular cylinder = R 2 Sum of area of two ends of the right circular cylinder = π R 2 2 + π R 2 2 = 2 π R 2 4 = π R 2 2 Area of the curved surface of the right circular cylinder = 2 π H × R 2 = π H R Given, the sum of the area of two ends of a right circular cylinder is equal to 1 3 of its curved surface. Therefore, π R 2 2 = 1 3 × π R H ⇒ R 2 = H 3 ⇒ H R = 3 2 ⇒ H : R = 3 : 2 Hence, the ratio of the height and diameter of the cylinder is 3 : 2 .

The sum of the area of two ends of a right circular cylinder is equal to 1 3 of its curved surface. Find ratio of the height and diameter of the cylinder.

Let the height of the right circular cylinder be H and the diameter of the right circular cylinder be R . Radius of the right circular cylinder = R 2 Sum of area of two ends of the right circular cylinder = π R 2 2 + π R 2 2 = 2 π R 2 4 = π R 2 2 Area of the curved surface of the right circular cylinder = 2 π H × R 2 = π H R Given, the sum of the area of two ends of a right circular cylinder is equal to 1 3 of its curved surface. Therefore, π R 2 2 = 1 3 × π R H ⇒ R 2 = H 3 ⇒ H R = 3 2 ⇒ H : R = 3 : 2 Hence, the ratio of the height and diameter of the cylinder is 3 : 2 .