What is the Formula for the Volume of a Sphere?

The radius of the sphere is the same as the radius of the cylinder's bases: 7 centimeters
A circle through the middle of the sphere is the same size as the cylinder's bases
The red V is the volume of the sphere and the black V is the volume of the cylinder
π is pi, r is radius, h is height
Since the sphere just touches the top and bottom of the cylinder, the height is equal to the diameter
Diameter = 2 times the radius, so h=2r
V=(2/3)(πr²)(2r) simplifies to V=(4/3)πr³

1. The sphere fits really well, barely touching the sides, top, and bottom of the cylinder
2. The radius is 7 centimeters
1. The volume of a sphere is just 2/3 the volume of a cylinder
2. Remember, the formula for the volume of a cylinder is πr²h
3. π is pi, which we can approximate to 3.14
4. 'r' is the radius, and 'h' is the height of the cylinder
5. V stands for volume and the red V is the volume of the sphere
6. But 'h' is the height of the cylinder, and we need things in terms of the sphere!
1. The volume of a cylinder is πr²h
2. π is pi, r is radius, h is the height of the cylinder
3. The sphere just touches the top and bottom of the cylinder
4. Just like a circle, the diameter of the sphere is twice the radius, or 2r
5. So we can substitute 2r for h
6. V is the volume of the sphere
7. We can use the commutative property to rearrange as (2/3)(2)πr²r
1. V is the volume of the sphere
2. π is pi, an irrational number that we can approximate to 3.14
3. r is the radius of the sphere, which is 7 cm
4. Using the order of operations: V=(4/3)(3.14)(343)
5. We've rounded the answer to two decimal places, so we use the ≈ symbol to mean 'approximately equal to'
6. The radius is given in centimeters, so our units are cm³, or centimeters cubed

What is the formula for the volume of a sphere?