Volume Of Sphere
Related Pages
Volume Formulas
Explanations For The Surface Area Formulas
Volume Of Cylinders
More GCSE Maths Lessons
More Geometry Lessons
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.
Spheres
Volume of a Sphere
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.
The volume of a sphere is the amount of three-dimensional space it occupies.
The following figure gives the formula for the volume of a sphere. Scroll down the page for examples and solutions.
Geometry Worksheets
Practice your skills with the following worksheets:
Printable & Online Geometry Worksheets
Formula for 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 formula for the volume (V) of a sphere is:
\(V = \frac{4}{3} πr^3 \)
Where:
V = Volume of the sphere
π (pi) is a mathematical constant, approximately 3.14159.
r = radius of the sphere (the distance from the center of the sphere to any point on its surface)
The formula for the surface area of sphere is:
A = 4πr2
How to calculate the volume of a sphere?
- Identify the radius (r):
If you’re given the diameter (d), remember that the radius is half of the diameter: r = d/2.
If you’re given the surface area (SA), you can find the radius using SA = 4πr2, so
\( r = \sqrt{\frac{SA}{4π}} \) - Cube the radius (r3) and multiply by 3/4 and π.
- The volume will always be in cubic units.
Example:
Calculate the volume of sphere with radius 4 cm.
Solution:
Volume of sphere
We can also change the subject of the formula to obtain the radius given the volume.
Example:
The volume of a spherical ball is 5,000 cm3. What is the radius of the ball?
Solution:
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 a hemisphere
What is a hemisphere?
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.
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.
Example:
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.
How to derive the formula of a sphere using calculus?
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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