Surface Area of Hemisphere
You must know that a hemisphere is a half of a sphere. The formulae below can be used to find the curved surface area of a hemisphere (without the base circle area) and the total surface area of a hemisphere (with the base circle area).
Curved Surface Area of Hemisphere:
You must know that the surface area of a sphere is 4πr².
A hemisphere is half of a sphere, this must mean that the curved surface area of a hemisphere is the surface area of a sphere divide by 2. That is; 4πr²/2 which gives the following expression.
This formula does not take into account the circular base
Curved Surface Area = 2πr²
The formula above does not take into account the entire surface area covered by the hemisphere because it does not account for the circular base below on the hemisphere. The formula below finds the total surface area.
Total Surface Area of Hemisphere
If you’re to take into account the circular base below the curve, you will need to use the formula below. The surface area would be a combination of the curve area and the area of the circle. You must know that the area of the circle is πr². This means the total surface area is 2πr² + πr².
Total Surface Area = 3πr²
Remember there is a difference between the curved surface area and the total surface area. The total surface area includes the base circle below the hemisphere and the curve surface area does not, it’s just the curve of the hemisphere.
Really helpful and nice work.
how do you find a curved surface area when height is given in the question…?????