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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
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:
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
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
The volume of a sphere is . Find the radius of the sphere.
Solution
The volume of a sphere is . Find the diameter of the sphere.
Solution
Find the volume of a sphere with diameter 2 units.
Solution
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:
- The volume, V of a sphere with diameter, d is given by the formula:
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Frequently Asked Questions about Volume of Sphere
What is the volume of a sphere?
The volume, V of a sphere with radius, r is given by the formula: V=(4/3)πr³
How to find the volume of a sphere?
The volume, V of a sphere with radius, r is given by the formula: V=(4/3)πr³
What is the formula for the volume of a sphere?
The volume, V of a sphere with radius, r is given by the formula: V=(4/3)πr³
How do you calculate the volume of sphere with diameter?
The volume, V of a sphere with radius, d is given by the formula: V=(1/6)πd³
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