Think of a soccer ball, think of a globe: these are round three-dimensional objects. The shape of such objects is referred to as a sphere. In this article, we will learn how to find the volume of a sphere.
Volume of a Sphere Meaning
To visualize a sphere, consider all possible congruent circles in space that have the same point for their center. Taken together, these circles form a sphere. All points on the surface of the sphere are an equal distance from its center. This distance is the radius of the sphere.
In space, a sphere is the locus of all points that are at a given distance from a given point – its center.
The total space occupied by a sphere is referred to as the volume of the sphere.
The Volume of a Sphere Formula
The formula to calculate the volume V of a sphere with radius r is
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Why do we use this formula to compute the volume of a sphere? You can relate finding the formula for the volume of a sphere to the volume of a right pyramid and the surface area of the sphere.
Suppose the space inside a sphere is separated into infinitely many near-pyramids, all with vertices located at the center of the sphere as shown below:
Fig. 1: The sphere as a combination of infinite near-pyramids
The height of these pyramids is equal to the radius r of the sphere. The sum of the areas of all the pyramid bases equals the surface area of the sphere.Each pyramid has a volume of ![]()
, where B is the area of the pyramid's base and h is its height. Then the volume of the sphere is equal to the sum of the volumes of all of the small pyramids.
Volume of a Sphere with Diameter
Suppose that instead of the radius, you are given the diameter of the sphere. Since the diameter is twice the radius, we can simply substitute the value ![]()
in the above formula. This would lead to:
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Volume of a Sphere Calculations with examples
Let us take a look at some calculations related to the volume of spheres.
Volume of Sphere Examples
we will be looking at several examples to give a good explanation about this topic
Find the volume of a sphere of radius 4.
Solution
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A great circle is when a plane intersects a sphere so that it contains the center of the sphere. In effect, a great circle is a circle contained within the sphere whose radius is equal to the radius of the sphere. A great circle separates a sphere into two congruent halves, each called a hemisphere.
Find the volume of a sphere whose great circle has an area of 154 unit2.
Solution
Area of the great circle ![]()
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The volume of a sphere is ![]()
. Find the radius of the sphere.
Solution
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The volume of a sphere is ![]()
. Find the diameter of the sphere.
Solution
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Find the volume of a sphere with diameter 2 units.
Solution
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Volume of Spheres - Key takeaways
- In space, a sphere is the locus of all points that are at a given distance from a given point called its center.
- The volume, V of a sphere with radius, r is given by the formula:
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- The volume, V of a sphere with diameter, d is given by the formula:
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