To find the volume of a sphere, use the formula:
V=43πr3V=\frac{4}{3}\pi r^3V=34πr3
where VVV is the volume and rrr is the radius of the sphere
Steps to Calculate the Volume of a Sphere:
- Determine the radius rrr of the sphere. If you only have the diameter ddd, divide it by 2 to get the radius: r=d2r=\frac{d}{2}r=2d
- Cube the radius: r3r^3r3.
- Multiply by π\pi π (approximately 3.1416).
- Multiply by 43\frac{4}{3}34.
- The result is the volume of the sphere in cubic units.
Example:
If the radius is 3 cm,
V=43×π×33=43×π×27≈113.1 cm3V=\frac{4}{3}\times \pi \times 3^3=\frac{4}{3}\times \pi \times 27\approx 113.1\text{ cm}^3V=34×π×33=34×π×27≈113.1 cm3
If you only know the circumference CCC, you can find the radius first:
r=C2πr=\frac{C}{2\pi}r=2πC
Then use the volume formula
. This formula is derived using calculus or by considering the sphere as composed of many thin circular disks stacked together
. In summary, the key formula is:
V=43πr3\boxed{V=\frac{4}{3}\pi r^3}V=34πr3
which gives the volume of a sphere when you know its radius
