UPSKILL MATH PLUS

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Learn more### Theory:

A cylinder emptied from the inner side and has a difference in the outer and inner radius of a cylinder with the same height is called a hollow cylinder.

**Properties of hollow cylinder**:

**1**. The inner and outer radius of the hollow cylinder is different.

**2**. The inner and outer lateral surface areas of the hollow cylinders are different.

**3**. The height of the inner and outer cylinders are the same.

Curved surface area of a hollow cylinder:

Let \(R\) be the outer radius, \(r\) be the inner radius, and \(h\) be the height of the hollow cylinder.

C. S. A. \(=\) Curved surface area of outer cylinder \(+\) Curved surface area of the inner cylinder

\(=\) \(2 \pi R h\) \(+\) \(2 \pi r h\)

\(=\) \(2 \pi (R + r)h\)

**Curved surface area of a hollow cylinder**\(=\) \(2 \pi (R + r)h\) sq. units

Total surface area of a hollow cylinder:

T. S. A. \(=\) Curved surface area \(+\) Area of a top circular ring \(+\) Area of a bottom circular ring

\(=\) \(2 \pi (R + r)h\) \(+\) \(\pi (R^2 - r^2)\) \(+\) \(\pi (R^2 - r^2)\)

\(=\) \(2 \pi (R + r)h\) \(+\) \(2\pi (R^2 - r^2)\)

\(=\) \(2 \pi (R + r)h\) \(+\) \(2\pi (R + r) (R - r)\)

\(=\) \(2 \pi (R + r) [h + (R - r)]\)

\(=\) \(2 \pi (R + r) (R - r + h)\)

**Total surface area of a hollow cylinder**\(=\) \(2 \pi (R + r) (R - r + h)\) sq. units