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 Sphere

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

Online Volume Calculator, click on the link will open a new window.