When a sphere is cut into two halves by a plane through the center, then these two equal parts are known as hemispheres. A hemisphere can be defined as a set of points in a three-dimensional space where all these points lie on a surface and are equidistant from the center. We will take a detailed look at the surface area and volume of hemisphere formula in this article. Additionally, we will see an example that will help us to solve questions. It is interesting to know that the Earth is in the form of a sphere. When the Earth is divided into two parts we get the Northern the Southern hemisphere.
Volume of a Hemisphere
We can define the volume of a hemisphere as the complete space that is contained within a hemisphere or the capacity. The volume of a hemisphere is usually measured in cubic units. We know the hemisphere is half the measurement of a sphere. This implies that the volume will be half of that of a sphere. The formula for a sphere’s volume is given by 4/3(?)(r)3, where r refers to the radius. This is the distance from the center of the hemisphere to any point on the surface. ? denotes a constant, the value of which is given by 22/7 or 3.14… (it is a non-terminating and non-repeating decimal value). Thus, we can now get the volume of a hemisphere.
Volume of a hemisphere = ½ * volume of a sphere
= ½ * 4/3(?)(r)3 = 2/3(?)(r)3
Surface Area of a Hemisphere
There are two types of surface areas when we talk about a hemisphere.
- Curved Surface Area (CSA)
- Total Surface Area (TSA)
Curved Surface Area (CSA)
The curved surface area of hemisphere is defined as the surface area occupied by only the curved surface. This area excludes the base. We know that the formula for the CSA of a sphere is given by 4 (?) r2. When we half this formula, we will get the measure of the CSA of a hemisphere.
CSA of hemisphere = ½ * CSA of a sphere = ½ [4 (?) r2] = 2 (?) r2
Total Surface Area (TSA)
The TSA of a hemisphere is defined as the complete surface area of the object, including the measure of the base. Thus, the formula for the TSA of a hemisphere can be derived by the addition of the area of the base and the CSA. Since the base is in the shape of a circle thus, the area is given by (?) r2.
TSA of a hemisphere = CSA + base = 2 (?) r2 + (?) r2 = 3 (?) r2
For instance, suppose we have a hemisphere with a radius = 14 cm, and we have to find the volume and surface area. The steps are listed below:
- Step 1: Volume = 2/3(?)(r)3. Substituting ? as 22/7 as the radius 14 is completely divisible by 7. We get the volume to be 5747 cm3.
- Step 2: CSA = 2 (?) r2 = 1232 cm2
- Step 3: TSA = 3 (?) r2 = 1848 cm2
Several figures have to be studied under the topic of surface areas and volumes. It is best for kids to join an educational platform such as Cuemath. The Math experts at Cuemath teach a well-organized curriculum, help kids develop a robust mathematical foundation, and ensure that every child has an enjoyable learning experience. Start your Cuemath journey in surface areas today!