Solid geometry is concerned with three-dimensional shapes.
In this lesson, we will learn
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 equal to four-thirds of the product of pi and the cube of the radius.
The volume and surface area of a sphere is given by the formulas:
where r is the radius of the sphere.
|Worksheet calculate the volume of spheres||Worksheet calculate the surface area of spheres|
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.
A hemisphere is half a sphere, with one flat circular face and one bowl-shaped face.
Volume of hemisphere
where r is the radius
This video shows how to find the volume of a hemisphere.
The following video shows how to solve problems involving the formulas for the area and volume of spheres.
A sphere has a volume of 288π. Find its area.
This video gives a review of the formula for determining the volume of a sphere accompanied by practice problems.
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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