Volume of a cone
Given the radius or r and the height or h, the volume of a cone can be found by using the formula:
Formula: V
_{cone} = 1/3 × b × h
b is the area of the base of the cone. Since the base is a circle, area of the base = π × r
^{2}
Thus, the formula to use to find the volume is V
_{cone} = 1/3 × π × r
^{2} × h
Use π = 3.14
Some examples that will show how to find the volume of a cone.
Example #1:
Calculate the volume if r = 2 cm and h = 3 cm
V
_{cone} = 1/3 × 3.14 × 2
^{2} × 3
V
_{cone} = 1/3 × 3.14 × 4 × 3
V
_{cone} = 1/3 × 3.14 × 12
V
_{cone} = 1/3 × 37.68
V
_{cone} = 1/3 × 37.68/1
V
_{cone} = (1 × 37.68)/(3 × 1)
V
_{cone} = 37.68/3
V
_{cone} = 12.56 cm
^{3}
Example #2:
Calculate the volume if r = 4 cm and h = 2 cm
V
_{cone} = 1/3 × 3.14 × 4
^{2} × 2
V
_{cone} = 1/3 × 3.14 × 16 × 2
V
_{cone} = 1/3 × 3.14 × 32
V
_{cone} = 1/3 × 100.48
V
_{cone} = 1/3 × 100.48/1
V
_{cone} = (1 × 100.48)/(3 × 1)
V
_{cone} = 100.48/3
V
_{cone} = 33.49 cm
^{3}
An example showing how to find the volume of an oblique cone.
Since the formula to find the volume of a cone applies to all cones, including oblique cone, we can use the formula V = 1/3(π×r^{2}×h)
Example #3:
Find the volume of an oblique cone with a diameter of 12 ft and a height of 15 ft. Before using the formula, we need to find the radius of the cone.
radius = diameter/2 = 12/2 = 6
V
_{oblique cone} = 1/3 × 3.14 × 6
^{2} × 15
V
_{oblique cone} = 1/3 × 3.14 × 36 × 15
V
_{oblique cone} = 1/3 × 3.14 × 540
V
_{oblique cone} = 1/3 × 1695.6
V
_{oblique cone} = 1/3 × 1695.6/1
V
_{oblique cone} = (1 × 1695.6)/(3 × 1)
V
_{oblique cone} = 1695.6/3
V
_{oblique cone} = 565.2 ft
^{3}
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