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Learn more### Theory:

Hemisphere

A section of the sphere cut by a plane through any of its great circles is a hemisphere. In another way, we can say, one half of a sphere is called a hemisphere.

Curved surface area:

C. S. A. \(=\) \(\frac{\text{Surface area of a sphere}}{2}\)

\(=\) $\frac{4\mathrm{\pi}{r}^{2}}{2}$

\(=\) \(2\pi r^2\)

**Curved surface area of a hemisphere**\(=\) \(2\pi r^2\) sq. units.

Total surface area:

T. S. A. \(=\) Curved surface area of a hemisphere \(+\) Area of the top region

\(=\) \(2\pi r^2\) \(+\) \(\pi r^2\)

\(=\) \(3 \pi r^2\)

**Total surface area of a hemisphere**\(=\) \(3 \pi r^2\) sq. units.

Hollow hemisphere

A hemisphere emptied from the inner side and has a difference in the outer and inner radius of a hemisphere is called a hollow hemisphere.

Curved surface area:

Let \(r\) be the inner radius and \(R\) be the outer radius of the hollow hemisphere.

The thickness of the hemisphere, \(t\) \(=\) \(R - r\)

C. S. A. \(=\) Area of an internal hemisphere \(+\) Area of an external hemisphere

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

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

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

T. S. A. \(=\) Curved surface area of a hollow hemisphere \(+\) Area of the ring formed

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

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

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

\(=\) \(3 \pi R^2\) \(+\) \(\pi r^2\)

\(=\) \(\pi(3R^2 + r^2)\)

**Total surface area of a hollow hemisphere**\(=\) \(\pi(3R^2 + r^2)\) sq. units

Important!

**The properties of a hemisphere are same as the properties of a sphere**.