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
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