Hemisphere

Meaning of Hemisphere 

When discussing the word hemisphere, the very first thing which comes to our mind is the two parts of the earth that is the southern and northern hemispheres. But here we are discussing geometry and not geography. So in geometric terms, a hemisphere is a 3D figure which is being cut off into two equal parts having one side flat. In layman’s terms, it is half of a sphere. Which means a sphere is divided into two equal parts. We all have seen, even ate hemispheres in our lives. Yes, it’s watermelons, lemons, melons, etc. Let’s discuss each and everything about the hemisphere to have a better understanding of it. 

Define Hemisphere 

When looking at the word hemisphere, it is a combination of two words Hemi and sphere. So in geometry, a hemisphere is a 3D shale that is exactly half of a sphere with a flat on one side and circular oval bowl-shaped structure. A hemisphere is made by cutting down a sphere into two equal parts from its Center. The flat part of the hemisphere is known as the base or face. Let’s now discuss the characteristics of a hemisphere. 

Characteristics of a Hemisphere 

As discussed above, a hemisphere is half a sphere and this is the reason why they both have almost identical characteristics. Below are mentioned the characteristics of a hemisphere. 

1. A hemisphere has a one-sided curved surface and therefore has a curved surface area. 
2. A hemisphere has a diameter that cuts the sphere into two equal parts by passing through the center and touching two opposite sites. 
3. A hemisphere doesn’t have any vertices or edges points like a sphere. 
4. When a plane interests at the center point of a sphere cutting them into two equal parts, then the great circle of the sphere creates. 
5. A hemisphere doesn’t consider a polyhedron because polyhedrons are made from polygons while a hemisphere is made from a sphere that has only one circular base and curved surface. 
6. The radius of a hemisphere can be identified as a line from the center point to its surface of it. 

Surface Area of a Hemisphere 

A hemisphere’s surface area can be defined as the area covered by the total surface of an object. Since we have discussed the hemisphere shape curved from one side and flat from another. A hemisphere has two classifications of surface area which is the total surface area and the curved surface area. So in simple terms, the surface area of a hemisphere is the total region covered by a hemisphere. As a hemisphere is half a sphere and is just like a sphere, therefore it can be hollow and solid (either of one). 

The surface area of a hemisphere has a formula to calculate it for both solid and hollow hemispheres. Since the surface area of the hemisphere is classified into two parts, we will be discussing each of them one by one for a better understanding. 

• Curved Surface Area of a solid Hemisphere 

A hemisphere’s curved surface area means the area or region covered or occupied by the curved part of the hemisphere. Since it is just a half part of a sphere, it can be calculated using radius. 

Curved Surface Area of a Hemisphere = (Curved Surface Area of a Sphere)½ 

Or

Curved Surface Area of a Hemisphere = ½(4πr²)

= 2πr²

Where, r = Radius of the Hemisphere 

• Total Surface Area of a solid hemisphere 

A hemisphere’s total surface area can be defined as the total space or region covered by the curved area as well as the base surface of the hemisphere. It can be easily calculated by calculating the total of areas of both curved surface and base surface. 

The total surface area of a hemisphere = Curved Surface Area + Base Area 

= 2πr² + πr²

= 3πr²

Where r = Radius 

• Surface Area of a Hollow Hemisphere 

A hollow hemisphere contains two radii for two circular bases, one of them is inside the circular base and another one is the outer circular base. So the formula to calculate both the circular base is:

Outer Curved surface area = 2πr2² 

Inner Curved Surface Area = 2πr1²

Area of the hollow ring = (r2²–r1²)π

Total Surface Area = 2πr2² + 2πr1² + π(r2²–r1²)

= 2π(r2²+r1²) + π(r2²–r1²) 

= 3πr2² + πr1²

Where, 

r1 = radius of the inner hemisphere.

r2 = radius of the outer hemisphere. 

Steps to calculate Hemisphere Surface Area 

Since we have discussed everything about a hemisphere right from its meaning to its surface area. The surface area of a solid hemisphere is of two types, curved and total surface area. While there is the only total surface area for a follow hemisphere. So after knowing this much, the last step that remains is the procedure to calculate the hemisphere surface area. Here are the steps to calculate hemisphere surface area: 

For curved surface area:

• Find out the radius (r) of the hemisphere. 

1. Then calculate the curved surface area with the help of the formula, 2πr². 
2. Do the calculation and the answer will be at your fingertips. 

For Total Surface Area:

1. Find out the radius (r) of the hemisphere. 
2. Then calculate the total surface area with the help of the formula, 3rπ². 
3. Do the calculation and the answer will be at your fingertips. 

For Surface Area (Hollow Hemisphere)

1. Find out the outer(r2) and inner(r1) radius of the hollow hemisphere. 
2. Then calculate the surface area of the hemisphere with the help of the formula, (3πr2²+πr1²). 
3. Do the calculation and the answer will be at your fingertips. 

Conclusion

Hemisphere is basically a half piece of a sphere whose diameter and radius remain the same as a sphere. It’s just a 3D figure which has a flat part on one side and a curved part on another side. This means hemisphere shape is one side curved and one-sided flat. So we have discussed every piece of detail about the hemisphere from meaning to the steps for calculating the surface area of it.