Curved Surface Area of a Cylinder Formula

Curved Surface Area of a Cylinder Formula

A cylinder is a 3D shape with circles on both its ends. Examples of a cylinder can be a pipe, pen, tank, etc. The curved surface area of a cylinder means area of the curved part of the cylinder i.e., area except both the circles at top and bottom.

A cylinder is made of two circles and a rectangle. When we fold a rectangle, the breadth becomes the height of the cylinder and the height becomes the circle. So, to derive the formula for the curved surface area of a cylinder, we need a formula for the area of the rectangle.

Area of a rectangle = breadth x height

Curved Surface Area of a Cylinder = Area of a rectangle = breadth x height = h x 2r = 2rh

Examples:

1. There is a cylindrical water tank with a height of 7 feet and radius of 3 feet. Find the curved surface area of the cylindrical water tank.

Given data: h = 7, r = 3

Curved surface area of the cylindrical water tank = 2rh = 2 x 22/7 x 3 x 7 = 132 sq. feet

2.  A cylindrical speaker has a curved surface area of 1848 sq. cm. It has a radius of 14 cm. Find the height of the cylindrical speaker.

Given data: Curved Surface Area of the speaker = 1848, r = 14

Curved surface area of the cylindrical speaker = 2rh

1848 = 2 x 22/7 x 14 x h

h = 21

3.  Kamal needs a cover for its bottle which is cylindrical in shape. Price of cover is 0.5 Rs per sq. cm, height of the bottle is 7 cm and radius of the bottle is 3.5 cm. Find how much a cover would cost to Kamal.

Given data: h = 7, r = 3.5, cost per sq. cm = 0.5 Rs.

For finding the cost of the cover, we need to find the curved surface area of the bottle.

Curved surface area of the cylindrical bottle = 2rh = 2 x 22/7 x 3.5 x 7 = 154 sq. cm

Cost of the bottle cover = 154 sq. cm x 0.5 Rs. = 77 Rs.