Surface Area of a Sphere Formula (original) (raw)
Last Updated : 23 Jul, 2025
A sphere can be called a three-dimensional equivalent of a circle. It is a collection of points in tri-space that are all at the same distance from a particular point. This distance is regarded as the radius of the said sphere. The Area of the Sphere can be calculated using the radius of the sphere.
**Surface Area of Sphere
The Surface area of a sphere (or simply the Area of Sphere) refers to the region covered by the sphere's outer surface. The three-dimensional version of a circle is known as a sphere. A sphere differs from a circle in the aspect that a circle is a two-dimensional (2D) shape, but a sphere is a three-dimensional (3D) shape. A sphere's surface area is measured in square units.
**Formula of **Surface Area of Square
**A = 4πr 2
where, **r is the radius of the sphere
and , π(pi) is a constant i.e. approximately equal to 3.141
**Sample Problems
**Problem 1. Find the surface area of a sphere whose radius is 5 m.
**Solution:
Given: r = 5 m
Since, A = 4πr2
= 4 × 3.14 × 52
= 4 × 3.14 × 25
**A = 314 m 2
**Problem 2. Find the surface area of a sphere of radius 10 m.
**Solution:
Given: r = 10 m
Since, A = 4πr2
= 4 × 3.14 × 102
= 4 × 3.14 × 100
**A = 1256 m 2
**Problem 3. What would be the cost of painting a sphere of radius 4.5 cm at INR 5 per sq. cm?
**Solution:
Given: r = 4.5 cm
TSA = 4πr2
= 4 × 3.14 × 4.52
= 254.47 cm2
So, total cost of painting the sphere = 254.47 × 5
= **INR 1272.35
**Problem 4. What would be the cost of painting a sphere of radius 3 cm at INR 12 per sq. cm?
**Solution:
Given: r = 4.5 cm
TSA = 4πr2
= 4 × 3.14 × 32
= 113.04 cm2
So, total cost of painting the sphere = 113.04 × 12
= **INR 1356.48
**Problem 5. Find the surface area of a sphere of radius 15 m.
**Solution:
Given: r = 15 m
Since, A = 4πr2
= 4 × 3.14 × 152
= 4 × 3.14 × 225
**A = 2826 m²
People Also Read:
Practice Problems
Q1 : Calculate the surface area of a sphere with a radius of 7 cm.
Q2 : A spherical balloon has a surface area of 314cm². What is the radius of the balloon?
Q3 : If the radius of a sphere is increased by 50%, by what percentage does the surface area increase?
Q4 : Find the surface area of a sphere with a diameter of 12 meters.
Q5 : Compare the surface areas of two spheres with radii 4 cm and 8 cm. How many times larger is the surface area of the larger sphere?
Q6 : How much material would be needed to cover a spherical dome with a radius of 10 meters?
Ans1 : 196π cm² or 615.75 cm²
Ans2 : 5 cm (approx..)
Ans3 : 125%
Ans4 : 144π m² or 452.39 m² (approx..)
Ans5 : 4 Times
Ans6 : 400π m² or 1256.64 m²
Conclusion
The formula for the surface area of a sphere, 4πr² not only offers a way to measure the "skin" of spherical objects but also serves up in understanding far more complex mathematical concepts and practical applications. Understanding its derivation and applications with deeper insights is useful for both theoretical and applied mathematics.