The surface area of a sphere is the number of square units that will exactly cover its surface.
The formula for the surface area of a sphere is given by:
A = 4r²π
where A represents the area and r represents the radius.
If you already know the surface area and need to find the radius, we can rearrange the above formula and solve it for r:
and now take the square root of both sides:
divide both sides with 4π
The volume of a sphere is the number of cubic units that will exactly fill the sphere.
Volume of a sphere is given by:
where V represents the volume and r is the radius.
Again, we can solve the above formula for r and thus find the radius if we are given the volume:
and now take the third root of both sides
divide both sides with
The shape with the smallest possible surface area for a given volume is a sphere. Or in other words, the sphere is a shape with the largest volume for a fixed surface area.
The sphere therefore appears in nature in water drops, bubbles, planets etc.
Find the surface area and the volume of a sphere with radius 5.
To do this, simply plug in r=5 into the formulas.
For the area:
We can plug in 3.14π for and get:
For the volume:
Again, we can plug in 3.14 for π and get:
Find the radius of a sphere with a volume of 65.42.
Now we’ll use the last formula provided above, the one solved for r. Plug in 65.42 for V and 3.14 for π: