Surface Area Of A Hemisphere

What is a Hemisphere?

A hemisphere is half of a sphere, formed when a plane cuts a sphere into two equal parts. Like a dome, a hemisphere has one flat circular base and a curved surface on top.

 

Table of Contents

• Surface Area of a Hemisphere Formula

• Curved Surface Area of Hemisphere

• Total Surface Area of Hemisphere

• Surface Area of a Hemisphere Examples

• Real-Life Applications of Hemisphere

• Fun Facts about Hemisphere

• Common Misconceptions

• Practice Questions

• Conclusion

• FAQs on Surface Area of a Hemisphere
  
  

 

Surface Area of a Hemisphere Formula

There are two key types of surface areas:

• Curved Surface Area (CSA)

• Total Surface Area (TSA)
  
  

Formulas:

• CSA = 2πr²

• TSA = 3πr²
  
  

Here,
π ≈ 3.14
r = radius of the hemisphere

 

Curved Surface Area of Hemisphere

This is the outer rounded area excluding the base.
CSA = 2πr²

Example: If r = 4 cm,
CSA = 2 × 3.14 × 4² = 100.48 cm²

 

Total Surface Area of Hemisphere

This includes the curved area and the base (which is a circle).
TSA = CSA + Area of base = 2πr² + πr² = 3πr²

Example:
If r = 4 cm,
TSA = 3 × 3.14 × 4² = 150.72 cm²

 

Surface Area of a Hemisphere Examples

Q1: Radius = 4 cm
CSA = 100.48 cm²
TSA = 150.72 cm²

Q2: Radius = 7 cm
CSA = 2 × 3.14 × 49 = 307.72 cm²
TSA = 3 × 3.14 × 49 = 461.58 cm²

 

Real-Life Applications of Hemisphere

• Helmets

• Igloos

• Earth’s representation (northern and southern hemispheres)

• Domes in architecture

• Bowls and dishes
  
  

Understanding the surface area of a hemisphere helps in packaging design, architecture, geography, and even sports.

 

Fun Facts about Hemisphere

• The Earth is approximately a sphere, but we divide it into hemispheres to study geography.

• The formula CSA = 2πr² is exactly half the surface area of a sphere.

• Hemispheres are used in satellite designs to cover a wide signal area.
  
  

 

Common Misconceptions

• Mistake: Thinking CSA = 3πr² (that’s TSA, not CSA)

• Mistake: Using πr² as the CSA (πr² is just the base area)

• Clarification: The hemisphere includes a flat circular base—so TSA ≠ CSA unless the base is excluded
  
  

 

Practice Questions

1. Find the CSA and TSA of a hemisphere with radius 10 cm.

2. A bowl is in the shape of a hemisphere. If its radius is 7 cm, what is its surface area?

3. A dome has a radius of 14 m. Find its CSA and TSA.

4. A hemisphere-shaped tent has a base diameter of 8 m. Find its total surface area.

5. If the CSA of a hemisphere is 314 cm², what is its radius?
   
   

 

Conclusion

The surface area of a hemisphere is key in understanding many real-life objects and 3D shapes. By using the formulas for CSA and TSA, you can solve various mathematical and practical problems involving hemispheres with ease.

 

Frequently Asked Questions on Surface Area of a Hemisphere

1: What is the surface area of a hemisphere?

 Ans: It includes the curved area (CSA = 2πr²) and total surface area (TSA = 3πr²).

2: What is the formula of curved surface area of a hemisphere?

 Ans: CSA = 2πr²

3: What is the total surface area of a hemisphere with radius 5 cm?

 Ans: TSA = 3πr² = 3 × 3.14 × 25 = 235.5 cm²

4: Why do we add base area in TSA?

 Ans: Because the base is a circle, and TSA includes all outer surfaces including base.

5: Are bowl and dome examples of hemispheres?

 Ans: Yes! They are real-life examples of hemispherical shapes.

 

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