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Volume of a Cone
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Geometry
> Volume of a Sphere
Volume of a Sphere
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A sphere is a threedimensional solid with no base, no edge, no face and no vertex. sphere is a round body with all points on its surface equidistant from the center. The volume of a sphere is measured in cubic units.
The volume of the sphere is defined as:
V = 4/3 × π × r
^{3}
= π × d
^{3}
/6
The radius of the sphere can be determined by isolating r from the above mentioned formula:
Example 1:
Calculate the radius of a sphere whose volume is 1000cm
^{3}
.
Solution
:
The formula to find the radius of a sphere formula is
Example 2:
Find the volume of a sphere of radius 9.6 m, rounding your answer to two decimal places.
Solution
:
In order to find the volume of a sphere, we need to insert the value of
r
in the formula:
V = 4/3 × π × r
^{3}
V = 4/3 × π × 9.6
^{3}
V = 3704.09 m
^{3}
So the volume of the sphere is 3704.09 m
^{3}
Example 3:
A rectangular block of metal has a dimension of 21 cm, 77cm and 24 cm. The block has been melted into a sphere. Find the radius of the sphere.
Solution
:
The volume of the solid rectangular block of metal is:
21 × 77 × 24 cm
^{3}
.
Let r be the radius of the sphere
Then the volume of the sphere is:
V = 4/3 × π × r
^{3}
Since the volume is unchanged, we have:
4/3 × π × r
^{3 }
= 21 × 77 × 24
r
^{3}
= (21 × 77 × 24)/(4/3 × π)
r = 21cm
Example 4:
A marble (shaped as a sphere) has a diameter of 1cm. What is the volume of the marble?
Solution:
V = π × d
^{3}
/6
V = π ×1
^{3}
/6
V = 0.5236
V = 0.52
So the volume of the marble is: 0.52 cm
^{3 }
Example 5:
The surface area of a solid sphere is 1254 square feet. Find the volume of the solid sphere.
Solution
:
The surface area of a solid sphere:
SA = 4 × π × r
^{2}
1254 = 4 × π × r
^{2}
r
^{2}
= 1254 / (
4 × π
)
r = 9.99 feet
The volume of the sphere is therefore:
V = 4/3 × π × r
^{3}
V = 4/3 × π × 9.99
^{3}
V = 4174.12 ft
^{3}
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