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Volume of a Cone
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Volume of an Ellipsoid
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Volume of a Sphere
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Volume of a Cylinder
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Volume of a Cuboid
Additional Formulas
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Perimeter of a Square
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Perimeter of a Rectangle
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Perimeter of a Polygon
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Perimeter of a Parallelogram
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Perimeter of a Circle
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Area of a Square
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Geometry
> Volume of a Cone
Volume of a Cone
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r: the radius of the base
h: height
The volume of a cone is given by:
V =
π
∙ r
^{2}
∙ h / 3,
where π
∙ r
^{2}
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
∙ r
^{2}
∙ h / 3
V =
π
∙ 8
^{2}
∙ 5 / 3
V =
1004.8 / 3 = 334.93 cm
^{3}
Thus, the volume of the cone is 334.93 cm
^{3}
.
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
∙ r
^{2}
∙ h / 3
V =
22/7
∙ 2.1
^{2}
∙ 6 / 3
V =
27.72 cm
^{3}
So, the volume of the cone is 27.72 cm
^{3}
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
∙ r
^{2}
∙ h / 3
r is the determine by D/2, which is: 8cm / 2 = 4cm, insert the value of r we have:
V =
π
∙ 4
^{2}
∙ 11 / 3
V = 552.64/3 cm
^{3}
V = 184.21 cm
^{3}
Thus the volume of the cone is 184.21 cm
^{3}
.
Example 4:
Find the height of a right circular cone whose volume is 169 cm
^{3}
and radius is 4cm
Solution
:
V = 1/3
∙
π
∙
r
^{2}
∙
h
V = 169 = 1/3
∙
3.14
∙
4
^{2}
∙
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 cm
^{3}
and the radius of the cone = 1cm, use π = 22/7
Solution
:
V = 1/3
∙
π
∙
r
^{2}
∙
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
∙
r
^{2}
∙
h = 1/3
∙22/7 ∙ 7 ∙ 7 ∙ 9 = 462 m
^{3}
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 dm
^{3}
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
∙
r
^{2}
∙
h
Volume = 1/3
∙ 22/7 ∙ 27 ∙ 27 ∙ 42
= 32076 dm
^{3}
Space allowed for 1 person =2916 dm
^{3}
Number of persons = 32076 / 2916 = 11 Persons.
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