Surface Area of a Hemisphere

Two-dimensional geometry is concerned with the cartesian plane's x-y axis in mathematics, but when we rotate the figures in 2D geometry, then we get figures of 3D geometry. Three-dimensional geometry is an extension of two-dimensional geometry that mainly has x,y and z in the plane, corresponding to length, width, and height. A hemisphere's surface area is defined as the region swept by the whole surface of the solid item. The hemisphere's surface area is divided into two parts: the overall or total surface area and the curved surface area. Both total surface area and curved surface area will be discussed in this article.

The surface area of a hemisphere is defined as the area covered by the hemisphere's surface. A hemisphere is a three-dimensional figure conceived by splitting a sphere along a plane that passes through the diameter and center of the sphere. In simpler terms, a hemisphere is half of a spherical figure. The hemisphere might be solid or hollow, and its surface area (like any other solid shape) is measured in square units. Real-life examples of hemispheres are bowls, the shell of a coconut, igloo, hat, ice cream scoop, and much more.

Curved Surface Area of a Hemisphere (CSA) Formula

The curved or rounded surface of the body is responsible for the CSA or curved surface area of any hemisphere. As we know, the hemisphere is half of a sphere; therefore, the CSA is exactly half of the CSA of a sphere. The curved surface area of a hemisphere with radius, say 'k', can be calculated using the formula mentioned below: CSA of a hemisphere = 1/2 (CSA of a perfect sphere from which the hemisphere is carved out) = 1/2 (4 π k 2 ) = 2 π k 2

Total Surface Area of a Hemisphere (TSA) Formula

The entire surface area, i.e., the area of the curved surface and the area of the circular base, produces the total surface area or TSA of a hemisphere. The total surface area is conceptualized as the addition of the area of its curved surface (CSA) and the area of the perfectly round base surface. For a hemisphere, if its radius ‘k’ is given, then its entire surface area can be given by:

TSA of a hemisphere = Curved Surface Area of that hemisphere + Base Area = 2 π k² + π k² = 3 π k²

Surface Area of a Hollow Hemisphere Formula

There are multiple cases when a hemisphere is not solid but hollow. You can find such hemispheres everywhere, like our eating bowls. They have a cavity in between them. Such hemispheres have two diameters present in them; one is known as the outer diameter ‘k 1 ’, and another one is known as the inner diameter ‘k 2 ’. A ring-like structure is formed in the base of the hollow hemispheres. The area of the hollow hemisphere can be formulated as: