Surface Area of a Sphere
In these lessons we will learn
- the formula of the surface area of a sphere.
- how to calculate the surface area of a sphere.
- how to calculate the surface area of a hemisphere.
- how to solve problems about the surface area of spheres.
- how to prove the formula of the surface area of a sphere.
Related Pages
Surface Area Of Spheres Worksheet
More Geometry Lessons
Surface Area of a Sphere
A sphere is a solid in which all the points on the round surface are equidistant from a fixed point, known as the center of the sphere. The distance from the center to the surface is the radius.
Surface area of a sphere is given by the formula:
Surface Area of sphere = 4πr2
where r is the radius of the sphere.
Example:
Calculate the surface area of a sphere with radius 3.2 cm
Solution:
Surface area of sphere
= 4π r2
= 4π (3.2)2
= 4 × 3.14 × 3.2 × 3.2
= 128.6 cm2
Worksheetto calculate the surface area of spheres.
How to find the surface area of a sphere?
Example:
Find the surface area of a sphere with r = 4 ft
How to calculate the surface area of a sphere given the radius or diameter?
Example:
Find the surface area of a sphere with diameter = 22 cm
Surface Area of a hemisphere
A hemisphere is half a sphere, with one flat circular face and one bowl-shaped face.
The surface area of a hemisphere is equal to the area of the curve surface plus the area of the circular base.
Surface area of hemisphere
= 
× surface area of sphere + area of base
= × 4π r2 + π r2 = 3π r2
Example:
Calculate the surface area of a hemisphere with radius 4 cm
Solution:
Surface area of hemisphere
= × surface area of sphere + area of base
= × 4π r2 + π r2
= 3π r2
= 3π (4)2
= 150.86 cm2
Problems about surface area of spheres
Problem: What is the radius of the sphere given the surface area?
Example: What is the radius of a sphere with a surface area of 900π?
Problem:
The surface area of a sphere is 5024 square meters. What is the volume of the sphere? Use 3.14 for pi. Round your answer to the nearest cubic meter.
Problem:
The radius of a sphere is tripled.
a) Describe the effect on the volume.
b) Describe the effect on the surface area.
Proof of the formula of the surface area of a sphere
This video demonstrates that the surface area of a sphere equals the area of 4 circles. (It is not a formal proof)
The formula for the surface of a sphere is derived by summing up small ring elements of area along its perimeter. (uses calculus)
These two videos explain the Archimedes method of deriving the surface area of a sphere.
Part1:
Part 2:
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