The total surface area of a solid cylinder is 616 cm 2 . If the ratio between its curved surface area and total surface area is 1 : 2; find the volume of the cylinder.

Given, Total surface area = 616 cm 2 ⇒ 2πr(h + r) = 616 ⇒ πr(h + r) = ⇒ πr(h + r) = 308 ..........(1) Ratio between its curved surface area and total surface area = 1 : 2 Substituting value of h in equation (1), we get : ⇒ πr(r + r) = 308 ⇒ πr.2r = 308 ⇒ 2πr 2 = 308 ⇒ πr 2 = 154 ⇒ = 154 ⇒ r 2 = ⇒ r 2 = 49 ⇒ r = ⇒ r = 7 cm ⇒ h = 7 cm. Volume of cylinder = πr 2 h = = 22 × 49 = 1078 cm 3 . Hence, volume of cylinder = 1078 cm 3 .

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Mathematics

The total surface area of a solid cylinder is 616 cm². If the ratio between its curved surface area and total surface area is 1 : 2; find the volume of the cylinder.

Mensuration

Related Questions

A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embarkment 2 m in width and 1.6 m in height. Find the depth of the circular tank.

The sum of the height and the radius of a solid cylinder is 35 cm and its total surface area is 3080 cm²; find the volume of the cylinder.

A cylindrical vessel of height 24 cm and diameter 40 cm is full of water. Find the exact number of small cylindrical bottles, each of height 10 cm and diameter 8 cm, which can be filled with this water.

Two solid cylinders, one with diameter 60 cm and height 30 cm and the other with radius 30 cm and height 60 cm, are melted and recasted into a third solid cylinder of height 10 cm. Find the diameter of the cylinder formed.

Mathematics

The total surface area of a solid cylinder is 616 cm2. If the ratio between its curved surface area and total surface area is 1 : 2; find the volume of the cylinder.

Mensuration

Related Questions

A circular tank of diameter 2 m is dug and the earth removed is spread uniformly all around the tank to form an embarkment 2 m in width and 1.6 m in height. Find the depth of the circular tank.

The sum of the height and the radius of a solid cylinder is 35 cm and its total surface area is 3080 cm2; find the volume of the cylinder.

A cylindrical vessel of height 24 cm and diameter 40 cm is full of water. Find the exact number of small cylindrical bottles, each of height 10 cm and diameter 8 cm, which can be filled with this water.

Two solid cylinders, one with diameter 60 cm and height 30 cm and the other with radius 30 cm and height 60 cm, are melted and recasted into a third solid cylinder of height 10 cm. Find the diameter of the cylinder formed.

The total surface area of a solid cylinder is 616 cm². If the ratio between its curved surface area and total surface area is 1 : 2; find the volume of the cylinder.

The sum of the height and the radius of a solid cylinder is 35 cm and its total surface area is 3080 cm²; find the volume of the cylinder.