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100 LearnersLast updated on October 28, 2025
Base Area of a Sphere
The base area of a sphere refers to the area of a great circle, which is a two-dimensional surface on a sphere. A sphere is a three-dimensional shape where every point on the surface is equidistant from the center.
What is the Base Area of a Sphere?
The base area of a sphere is the area of a great circle. A sphere is a 3-dimensional shape with a continuous curved surface.
The base area of a sphere is essentially the area of a circle that passes through the center of the sphere, dividing it into two equal halves.
What is the Base Area of a Sphere Formula?
The base area of a sphere can be found using the formula for the area of a circle.
The formula for the base area is πr², where r is the radius of the sphere. The value of π is approximately 3.1416.
How to Find the Base Area of a Sphere?
The base area of a sphere 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 sphere and denote it as r.
Step 2: Use the formula πr² to calculate the base area. If the diameter is given instead of the radius, use the formula (π/4)D².
Step 3: Write the answer with square units.
For example, if the radius of a sphere 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 Sphere
Here are some tips and tricks to help solve the problem easily:
- Remember, the base is a circle.
- Always square the radius first.
- Use the correct π value.
- Check the units are in square units.
- Do not confuse with the total surface area of the sphere.
Common Mistakes and How to Avoid Them on the Base Area of the Sphere
When finding the base area of the sphere, students often make small mistakes, leading to incorrect answers. Here are some common mistakes that should 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 confuse the base area with the total surface area or volume formula. The base area of a sphere is the area of its great circle, 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 total surface area instead of the base
Students mistakenly calculate the total surface area (4πr²) instead of the base area (πr²). Always check whether the question asks for the base area or the total surface area.
Solved Examples for Base Area of the Sphere
Problem 1
The radius of a sphere is 3 cm. Find the base area.
28.26 cm²
Explanation
To find the base area of the sphere, use the formula πr².
The value of π is 3.14.
Radius is r = 3.
πr² = 3.14 × 3² = 3.14 × 9 = 28.26 cm²
Problem 2
Radius = 4.5 cm. Find the base area of a sphere.
63.62 cm²
Explanation
To find the base area of the sphere, Using the formula for base area is πr².
Radius = 4.5 cm.
The value of π is 3.1416.
The base area = πr² = 3.1416 × 4.5² = 3.1416 × 20.25 = 63.6174 = 63.62 cm²
Problem 3
A spherical balloon has a diameter of 8 cm. Find the base area.
50.24 cm²
Explanation
The diameter of the sphere is 8 cm. Radius = Diameter ÷ 2 Radius = 8 ÷ 2 = 4 cm.
Then find the base area = πr² = 3.14 × 4² = 3.14 × 16 = 50.24 cm²
Problem 4
The base area is 50.24 cm². Find the radius.
r = 4 cm
Explanation
To find the radius, use A = πr². 50.24 = 3.14 × r² r² = 50.24 / 3.14 r² = 16
Take the square root of both sides: r = √16 r = 4 cm
Problem 5
A glass sphere has a base radius of 7.8 cm. Find the base area to determine the area of the great circle.
191.3 cm²
Explanation
The formula for the base area of a sphere = πr².
r = 7.8 cm. π = 3.14.
Base area = πr² = 3.14 × (7.8)² = 3.14 × 60.84 = 191.3 cm²
FAQs on Base Area of the Sphere
1.What is the base area of the sphere?
2.What is the formula for the base area of the sphere?
3.What is the formula for the base area of a sphere with a diameter?
4.Is the base area the same as the total surface area of a sphere?
5.What unit is used for the base area of the sphere?
Important Glossary for Base Area of a Sphere
- Base Area: The area of the great circle that divides the sphere into two equal halves, calculated using the formula πr².
- Sphere: A 3-dimensional shape where every point on the surface is equidistant from the center.
- Great Circle: The largest possible circle that can be drawn on a sphere, passing through its center.
- Radius: The distance from the center of the sphere to any point on its surface.
- Diameter: The distance across the sphere, passing through its center; equal to twice the radius (D = 2r).
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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
