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101 LearnersLast updated on October 28, 2025
Base Area of a Hemisphere
The base area of a hemisphere refers to the area of the circular surface at the flat bottom. A hemisphere is essentially half of a sphere, with one flat circular face and one curved surface.
What is the Base Area of a Hemisphere?
The base area of a hemisphere is simply the area of the circle that forms its flat face. A hemisphere has one curved surface and one flat circular surface.
The surface area of a hemisphere includes both the curved surface and the base surface.
What is the Base Area of a Hemisphere Formula?
The base of a hemisphere is a circle, so we use the formula for the area of a circle to find the base area.
The formula for the base area is πr², where r = radius of the base and π is approximately 3.1416.
How to Find the Base Area of a Hemisphere?
The base area of the hemisphere formula is πr². This formula can be used to find the base area by following these steps:
Step 1: First, determine the radius of the hemisphere and denote it as r.
Step 2: If the radius is given, then find the base area of the hemisphere using the formula πr². If the diameter is given instead of the radius, use the formula π(D/2)².
Step 3: Write the answer with square units.
For example, if the radius of a hemisphere's base is 6 cm, find the base area: Base area = πr² = π × 6² = 3.1416 × 36 = 113.1 cm²
Tips and Tricks for the Base Area of the Hemisphere
Here are some tips and tricks to help solve the problem easily:
- Remember, the base is a circle.
- Square the radius first.
- use the right π value.
- Check the units.
- Don’t confuse with total surface area.
Common Mistakes and How to Avoid Them on the Base Area of the Hemisphere
When finding the base area of the hemisphere, students make small mistakes, leading to incorrect answers. Here are some common mistakes that can be avoided.
Mistake 1
Confusing radius with diameter
Students often mistakenly use the diameter directly in the formula instead of the radius. Always check whether the given measurement is the radius or the diameter before substituting it.
Mistake 2
Using the wrong formula
Some students mix up the base area with the surface area or volume formula. The base area of a hemisphere is the area of its circular base, calculated using the formula πr².
Mistake 3
Forgetting to square the radius
First, square the radius (r²), then multiply the result by π to find the base area.
Mistake 4
Using the wrong value of π
Sometimes students use an incorrect value for π. Use π = 3.1416 for decimals and 22/7 when working with fractions.
Mistake 5
Calculating the curved surface instead of the base
Students mistakenly use the formula 2πr² instead of πr² for the base area. Always check whether the question is asking for the base area or the curved surface area.
Solved Examples for Base Area for the Hemisphere
Problem 1
The radius of a hemisphere's base is 5 cm. Find the base area.
78.54 cm²
Explanation
To find the base area of the hemisphere, use the formula πr².
The value of π is 3.1416.
Radius is r = 5.
πr² = 3.1416 × 5² = 3.1416 × 25 = 78.54 cm²
Problem 2
Radius = 7 cm. Find the base area for the hemisphere.
153.94 cm²
Explanation
To find the base area for the hemisphere: Using the formula for the base area of the hemisphere is πr².
Radius = 7. The value of π is 3.1416.
The base area for the hemisphere = πr² = 3.1416 × 7² = 3.1416 × 49 = 153.9364 = 153.94 cm²
Problem 3
The open end of a bowl has a diameter of 10 cm. Find the base area of the hemisphere.
78.54 cm²
Explanation
The diameter of the hemisphere is 10 cm. Radius = Diameter ÷ 2.
Radius of the hemisphere = 10 ÷ 2 = 5 cm.
Then find the base area of the hemisphere = πr². r² = 5 = 5². r² = 25.
The base area = 3.1416 × 25 = 78.54 cm².
Problem 4
The base area is 78.54 cm². Find the radius.
r = 5 cm
Explanation
To find the radius, A = πr². 78.54 = 3.1416 × r². r² = 78.54 ÷ 3.1416. r² = 25.
Take the square root of both sides. r = √25. r = 5 cm.
Problem 5
A spherical cap with a base radius of 6.3 cm. Find the base area to determine the cover size.
124.7 cm²
Explanation
The formula for the base area of a hemisphere = πr². r = 6.3. π = 3.1416.
Base area = πr² = 3.1416 × (6.3)² = 3.1416 × 39.69 = 124.7 cm²
FAQs on Base Area for the Hemisphere
1.What is the base area of the hemisphere?
2.What is the formula for the base area of the hemisphere?
3.What is the formula for the base area of a hemisphere with a diameter?
4.Is the base area the same as the total surface area of a hemisphere?
5.What unit is used for the base area of the hemisphere?
Important Glossary for Base Area of a Hemisphere
- Base Area: The area of the flat circular surface at the bottom of a hemisphere, calculated using the formula πr².
- Hemisphere: A 3-dimensional shape that is half of a sphere, with one flat circular base and one curved surface.
- Radius: The distance from the center of the base to any point on its edge.
- Diameter: The distance across the circular base, passing through its center; equal to twice the radius (d = 2r).
- π (Pi): A mathematical constant approximately equal to 3.1416, used to calculate the area of circles.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
