Surface Area of Hemisphere – Formula and Examples

Here you will learn what is the formula for surface area of hemisphere (total and curved surface area of hemisphere) with examples.

Let’s begin –

What is Hemisphere ?

Let us take a solid sphere, and slice it exactly ‘through the middle’ with a plane that passes through its centre. It gets divided into two equal parts which is called a hemisphere. (Because ‘hemi’ means ‘half’)

Formula for Surface Area of Hemisphere

(i) Curved Surface Area of Hemisphere

Curved Surface Area (CSA) = \(2\pi r^2\)

(ii) Total Surface Area of Hemisphere

Total Surface Area (TSA) = \(3\pi r^2\)

Example : Find (i) the curved surface area and (ii) the total surface area of a hemisphere of radius 21 cm. 

Solution : Here, radius = 21 cm

(i) The curved surface area of a hemisphere of radius 21 cm would be 

CSA = \(2\pi r^2\) = \(2 \times {22\over 7} \times 21 \times 21\) = 2772 \(cm^2\)

(ii) The total surface area of the hemisphere of radius 21 cm would be 

TSA = \(3\pi r^2\) = \(3 \times {22\over 7} \times 21 \times 21\) = 4158 \(cm^2\)

Example : Find (i) the curved surface area and (ii) the total surface area of a hemisphere of diameter 70 cm. 

Solution : Here, diameter = 70 cm \(\implies\) radius r = 35 cm

(i) The curved surface area of a hemisphere of radius 35 cm would be 

CSA = \(2\pi r^2\) = \(2 \times {22\over 7} \times 35 \times 35\) = 7700 \(cm^2\)

(ii) The total surface area of the hemisphere of radius 35 cm would be 

TSA = \(3\pi r^2\) = \(3 \times {22\over 7} \times 35 \times 35\) = 11550 \(cm^2\)

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