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 \(cm^2\)
