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# Cylinder

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#### Cylinder - Lesson Summary

A cylinder can be defined as a solid figure that is bound by a curved surface and two flat circular surfaces. The flat surfaces are made up of two congruent circles that are parallel to each other. These flat surfaces are called the bases of the cylinder. The radius of the circular bases is the radius of the cylinder. The perpendicular line that passes through the centres of the two circular bases is the height of the cylinder or axis of the cylinder. A cylinder is said to be right circular cylinder if axis of the cylinder is perpendicular to the radius of the cylinder.

Curved surface area of a cylinder (CSA)

The curved surface joining the two bases of a right circular cylinder is called its lateral surface. If the curved surface of a cylinder is unfold, it opens up to become a rectangular sheet. The curved surface area of a cylinder is equal to the area of this sheet.

Area of a rectangle = length x breadth.

The length of the rectangular sheet is equal to the circumference of the base of the cylinder, which is equal to 2πr and the breadth of the rectangular sheet is equal to the height of the cylinder.

Substituting length = 2πr and breadth = h, we get

Area of the rectangular sheet = 2πr × h = 2πrh

∴ Curved surface area of a cylinder (CSA) = 2πrh.

Total surface area of a cylinder

Total surface area of a cylinder (TSA) = Curved surface area (CSA) + Total area of the flat surfaces

The flat surfaces of a cylinder are made up of two congruent circles.

∴ Area of the flat surface of a cylinder = Area of the base = πr2

Total area of both the flat surfaces = 2πr2

Total surface area of a cylinder (TSA) = 2πrh + 2πr2 = 2πr(h + r).

Volume of a cylinder

Volume of a cylinder = Area of the base × height

= πr2 × h (∵ Area of the base = πr2)

∴ Volume of a cylinder (V) = πr2h. 