Surface Area of a Sphere

In this lesson 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.

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 centre of the sphere. The distance from the centre 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

Worksheet to calculate the surface area of spheres.

This video shows how to calculate the surface area of a sphere given a radius.

The following video shows how to find the surface area of a sphere.

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?

Problem: The surface area of a sphere is 5024 square meters. What is the volume of the sphere?

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:

Custom Search

© Copyright 2005, 2012 - onlinemathlearning.com
Embedded content, if any, are copyrights of their respective owners.