To find the volume of a cone, use the formula:
V=13πr2hV=\frac{1}{3}\pi r^2hV=31πr2h
where:
- rrr is the radius of the circular base of the cone,
- hhh is the perpendicular height of the cone,
- π\pi π is approximately 3.14159.
Steps to calculate the volume of a cone:
- Measure or identify the radius rrr of the base of the cone.
- Measure or identify the height hhh of the cone (the perpendicular distance from the base to the tip).
- Substitute the values into the formula V=13πr2hV=\frac{1}{3}\pi r^2hV=31πr2h.
- Calculate the volume by squaring the radius, multiplying by the height, multiplying by π\pi π, and then taking one-third of that product.
- Express the answer with cubic units corresponding to the units used for radius and height.
Example:
If a cone has a radius of 3 cm and a height of 12 cm, then:
V=13π(3)2(12)=13π×9×12=36π≈113.1 cm3V=\frac{1}{3}\pi (3)^2(12)=\frac{1}{3}\pi \times 9\times 12=36\pi \approx 113.1\text{ cm}^3V=31π(3)2(12)=31π×9×12=36π≈113.1 cm3
This means the volume of the cone is approximately 113.1 cubic centimeters
Additional notes:
- The volume of a cone is exactly one-third the volume of a cylinder with the same base radius and height.
- If you know the diameter ddd instead of the radius, use r=d2r=\frac{d}{2}r=2d.
- If you have the slant height LLL instead of the perpendicular height, you can find the height using the Pythagorean theorem: h=L2−r2h=\sqrt{L^2-r^2}h=L2−r2
This formula and method provide a straightforward way to find the volume of any cone.
