how to find the volume of a sphere

To find the volume of a sphere, use the formula:

V=43πr3V=\frac{4}{3}\pi r^3V=34​πr3

where VVV is the volume and rrr is the radius of the sphere. The radius is half the diameter, so if you know the diameter ddd, then r=d2r=\frac{d}{2}r=2d​.

Steps to calculate the volume:

1. Determine the radius rrr of the sphere (half the diameter if only diameter is known).
2. Cube the radius: r3r^3r3.
3. Multiply by π\pi π (approximately 3.1416).
4. Multiply by 43\frac{4}{3}34​.

Example:

If the diameter is 14 cm, then the radius r=7r=7r=7 cm.

V=43π(7)3=43×π×343≈1436.8 cm3V=\frac{4}{3}\pi (7)^3=\frac{4}{3}\times \pi \times 343\approx 1436.8\text{ cm}^3V=34​π(7)3=34​×π×343≈1436.8 cm3

This gives the volume in cubic centimeters

Alternative formula using diameter:

You can also use the formula directly in terms of diameter:

V=πd36V=\frac{\pi d^3}{6}V=6πd3​

which comes from substituting r=d2r=\frac{d}{2}r=2d​ into the volume formula

. This method allows you to calculate the volume easily if you know either the radius or the diameter of the sphere.