To find the surface area of a sphere when you know its volume, you can use a couple of mathematical relationships between these two properties.
The volume (V) of a sphere is given by the formula:
V = (4/3)πr³
where r is the radius of the sphere.
Similarly, the surface area (A) of a sphere is given by the formula:
A = 4πr²
Here’s how you can find the surface area:
- Start with the volume of the sphere. Rearrange the volume formula to solve for the radius: r = ((3V)/(4π))^(1/3).
- Plug this value of r into the surface area formula:
- A = 4π((3V)/(4π))^(2/3).
By simplifying this expression, you can calculate the surface area directly using the volume of the sphere.
For example, if the volume of your sphere is 100 cubic units, you would first calculate the radius:
r = ((3 * 100)/(4 * π))^(1/3) ≈ 2.157.
Next, plug this back into the surface area formula:
A ≈ 4π(2.157)² ≈ 58.848.
So the surface area of the sphere would be approximately 58.848 square units.