How to show the surface area of a sphere is 4πr²

To play this video you need to enable JavaScript in your browser.

This video can not be played

A short video on how to show the surface area of a sphere with radius 'r' is 4πr². The area of a circle is πr². The surface area of the sphere is equal to 4 circles of the same radius.

Surface area of a sphere

Skip image gallery

Image caption,
Click to see a step-by-step slideshow.
Image caption,
WHAT YOU NEED: an orange, pencil and paper. The orange should be as round as possible, so the peel represents the surface area of a sphere.
Image caption,
STEP 1: Draw a circle around the orange. The circle should have the same radius as the orange.
Image caption,
STEP 2: Repeat this 3 more times. You should now have 4 identical circles. Each circle has area πr², so the total area of the 4 circles is 4πr².
Image caption,
STEP 3: Peel the orange and break the peel into small pieces.
Image caption,
STEP 4: Distribute the peel evenly and place into the 4 circles. It should all just fit.
Image caption,
You’ve done it! You’ve managed to show that the surface area of a sphere is 4πr².

Where next?

Want to dive deeper? Explore more with Bitesize.

Shape, space and measures

Surface area of a sphere

Where next?

More on Shape, space and measures