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Volume of a Sphere

A sphere is a three-dimensional 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 × r3 = π × d3/6

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 1000cm3.
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 × r3
V = 4/3 × π × 9.63
V = 3704.09 m3
So the volume of the sphere is 3704.09 m3

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 cm3.
Let r be the radius of the sphere
Then the volume of the sphere is:
V = 4/3 × π × r3
Since the volume is unchanged, we have:

4/3 × π × r3 = 21 × 77 × 24
r3 = (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 × d3/6
V = π ×13/6
V = 0.5236
V = 0.52
So the volume of the marble is: 0.52 cm3


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 × r2
1254 = 4 × π × r2
r2 = 1254 / (4 × π)
r = 9.99 feet

The volume of the sphere is therefore:

V = 4/3 × π × r3
V = 4/3 × π × 9.993
V = 4174.12 ft3

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