determine the surface area of each sphere to the nearest unit
Answers
The surface area of a sphere is given by the formula
Area = 4 π r 2
Where r is the radius of the sphere. In the figure above, drag the orange dot to change the radius of the sphere and note how the formula is used to calculate the surface area.
This formula was discovered over two thousand years ago by the Greek philosopher Archemedes. He also realized that the surface area of a sphere is exactly equal to the area of the curved wall of its circumscribed cylinder, which is the smallest cylinder that can contain the sphere. See Surface area of a cylinder.
If you know the surface area
By rearranging the above formula you can find the radius:
r = √a÷4 π
where a is the surface area.
Interesting facts
For a given volume, the sphere is the shape that has the smallest surface area. This why it appears in nature so much, such as water drops, bubbles and planets.
The surface area of a sphere is exactly four times the area of a circle with the same radius. You can see this in the area formula, since the area of a circle is
π r 2
and the surface area of a sphere is
4 π r 2