![sphere in cylinder](/sites/default/files/field/image/sphere-in-cylinder.jpg)
To calculate the volume of a sphere, you can use the formula:
Where:
- V is the volume of the sphere
- π (pi) is a constant approximately equal to 3.14159
- r is the radius of the sphere
How was the formula derived?
Actually, the formula for the volume of a sphere can be derived using calculus or using geometric method.
Here's an explanation:
- Imagine a sphere with radius r.
- Imagine a cylinder with radius r, and height h = r * 2.
- Place the sphere into the cylinder.
The volume of a cylinder is given by , where r is the radius of the cylinder and h is its height.
The diameter of the sphere is twice the radius, so the height of the cylinder is 2r.
Thus, the volume of the cylinder is .
However, the sphere only fills about two-thirds of this cylinder. So, the volume of the sphere is two-thirds of the cylinder's volume:
And that's where the formula comes from, by simply multiplying both sides by .