Recently Added Math Formulas

· Volume of a Cone
· Volume of an Ellipsoid
· Volume of a Sphere
· Volume of a Cylinder
· Volume of a Cuboid

Additional Formulas

· Perimeter of a Square
· Perimeter of a Rectangle
· Perimeter of a Polygon
· Perimeter of a Parallelogram
· Perimeter of a Circle
· Area of a Square
· Area of a Rectangle
· Area of a Polygon
· Area of a Triangle
· Area of a Parallelogram

Current Location > Math Formulas > Geometry > Volume of a Cone

Volume of a Cone

r: the radius of the base
h: height

The volume of a cone is given by:
V = π ∙ r² ∙ h / 3,
where π ∙ r² is the base area of the cone.

π defines the ratio of any circle's circumference to its diameter and is approximately equal to 3.141593, however the value 3.14 is often used.

Example 1: Find the volume of cone, whose radius is 8 cm and height is 5 cm.
Solution:

The formula to find the volume of cone is given by:
V = π ∙ r² ∙ h / 3
V = π ∙ 8² ∙ 5 / 3
V = 1004.8 / 3 = 334.93 cm³

Thus, the volume of the cone is 334.93 cm³.

Example 2: Find the volume of a cone whose base radius is 2.1 cm and height is 6 cm using π = 22/7
Solution:

The volume of a cone is defined as:
V = π ∙ r² ∙ h / 3
V = 22/7 ∙ 2.1² ∙ 6 / 3
V = 27.72 cm³
So, the volume of the cone is 27.72 cm³

Example 3: Find the volume of a cone, whose diameter is 8 cm and the height is 11 cm.
Solution:

As in previous examples:
V = π ∙ r² ∙ h / 3

r is the determine by D/2, which is: 8cm / 2 = 4cm, insert the value of r we have:
V = π ∙ 4² ∙ 11 / 3
V = 552.64/3 cm³
V = 184.21 cm³

Thus the volume of the cone is 184.21 cm³.

Example 4: Find the height of a right circular cone whose volume is 169 cm³ and radius is 4cm
Solution:
V = 1/3 ∙ π ∙ r² ∙ h
V = 169 = 1/3 ∙ 3.14 ∙ 4² ∙ h
V = 169 = 16.75 ∙ h
V = h = 169/16.75
V = h = 10.09 cm
The height of the right circular cone is 10.09 cm.

Example 5: Find the height of a cone whose volume is 22 cm³ and the radius of the cone = 1cm, use π = 22/7
Solution:
V = 1/3 ∙ π ∙ r² ∙ h = 22
V = 1/3 ∙ 22/7 ∙ 1 ∙ 1∙ h = 22
V = h = (22 ∙ 7 ∙ 3)/22
V = h = 21 cm.

Example 6: The circumference of the base of a 9 m high conical tent is 44 m. find the volume of the air contained in it, use π = 22/7
Solution:
Circumference of the base:
P = 2 ∙ π ∙ r = 44m
r = P / ( 2 ∙ π )
r = 44 / ( 2 ∙ π ) = 7 m

Height of the conical tent = 9m
Volume of air = 1/3 ∙ π ∙ r² ∙ h = 1/3 ∙22/7 ∙ 7 ∙ 7 ∙ 9 = 462 m³

Example 7: The vertical height of a conical tent is 42 dm and the diameter of its base is 5.4 m.
Determine the number of persons it can accommodate if each person uses 2916 dm³ of space use π = 22/7
Solution:
Height: h = 42 dm
Diameter: = 5.4 m = 54 dm
Radius: r = D/2 = 27 dm
Volume = 1/3 ∙ π ∙ r² ∙ h
Volume = 1/3 ∙ 22/7 ∙ 27 ∙ 27 ∙ 42 = 32076 dm³

Space allowed for 1 person =2916 dm³
Number of persons = 32076 / 2916 = 11 Persons.