Cones are three-dimensional shapes that have one circle that tapers to a point. When finding the volume of a cone, you use the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height. Notice the similarities and differences in this formula and the volume of a cylinder. What do you think it means? A cylinder with the same base as a cone is 3 times larger than the cone.
Sometimes, you won't be given a radius. You'll be given a diameter. The radius is equal to half the diameter. On the figure pictured, label the radius, the diameter, and the height.
Volume of a Cone Example 1
Find the volume of the following cone:
V = ?
π = 3.14
r = 21
h = 28
V = (1/3) * 3.14 * 21² * 28
V = 12924.24 cm³
Volume of a Cone Example 2
Find the volume of the following cone using the exact value:
V = ?
Example 1: Find the height of a cone if the cone's volume is 376.8 in³ and the radius is 6 in. Use 3.14 for pi.
V = πr²h
V = 376.8
π = 3.14
376.8 = (3.14) * (6)² * h
h = 376.8 / 37.68
h = 10 in
Given:
r = 6.5
h = 32
V = π(6.5)²(32)
V = 450.67 π in³
Sometimes, you will be asked to find a missing dimension. If you are missing a dimension, you will plug into your volume formula and solve for the missing variable.
Finding the Diameter of a Cone Example 1
Find the diameter of a cone if the height is 12 meters and the volume is 314 m³.
V = 314
314 = (1/3)π(12)²d
d = ?
12.56 = 314 / d
d = 314 / 12.56
d = 25
d = 10 m
