Solid geometry is concerned with three-dimensional shapes.
In these lessons, we will learn
- how to find the volume of a sphere.
- how to find the volume of a hemisphere.
- how to prove the formula for the volume of a sphere.
Related Topics: More Geometry Lessons
What is a sphere?
is a solid with all its points the same distance from
the center. The distance is known as the radius of the sphere. The maximum straight distance through the center of a sphere is known as the diameter of the sphere. The diameter is twice the radius.
How to find the volume of a sphere?
The volume of a sphere is equal to four-thirds of the product of pi and the cube of the radius.
The volume and surface area of a sphere are given by the formulas:
where r is the radius of the sphere.
Calculate the volume of sphere with radius 4 cm.
Volume of sphere
We can also change the subject of the formula to obtain the radius given the volume.
The volume of a spherical ball is 5,000 cm3. What is the radius of the ball?
The following videos explain how to use the formula to calculate the volume of a sphere.
Example: Find the volume of a sphere with a diameter of 14 cm.
Volume of spheres
Example: Find the volume of a sphere with a diameter of 12 cm.
Volume of a hemisphere
What is a hemisphere?
is half a sphere, with one flat circular face and one bowl-shaped face.
How to find the volume of a hemisphere?
The volume of a hemisphere is equal to two-thirds of the product of pi and the cube of the radius.
The volume of a hemisphere is given by the formula:
where r is the radius
This video shows how to find the volume of a hemisphere.
Example: Find the volume of a fishbowl with a diameter of 33cm.
How to solve word problems about spheres?
The following video shows how to solve problems involving the formulas for the surface area and volume of spheres.
A sphere has a volume of 288π. Find its area. Leave you answer in terms of π
Example: A ball has a diameter of 18 cm.
a) Sketch a cylinder that fits the ball and label its height and base.
b) What is the volume of the cylinder?
c) What is the volume of the ball?
Example: The cylinder is melted down into a sphere of radius r. Find an expression for r in terms of x.
How to proof the Formula of the Volume of a Sphere
This video gives a proof for the formula of the volume of a sphere that does not involve calculus. This is an "approximated" proof. You would need to use calculus for a more rigorous proof.
This video derives the formula of a sphere using calculus.
This video shows how Archimedes derived the volume of a sphere. To do so, he had to use a formula for the volume of a cone
You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.