Volume of a Sphere
Let's try an activity regarding the volume of a sphere.
Activity: Take spheres of different radii and a container filled with water upto the brim. Place the filled up container in a trough to collect the displaced water.
Now, one at a time, place the sphere in the container and let the displaced water fall into the trough. After every trial for different spheres, measure the amount of water overflown into the trough. Also, calculate the value for
The amount of water displaced will be equal to the value of
Volume of a Sphere =
where r is the radius of the sphere.
What about the volume of a hemisphere? We know that the hemisphere is one half of a split sphere. Thus,
Volume of a Sphere =
where r is the radius of the hemisphere.
Example 10: Find the volume of a sphere of radius 11.2 cm.
Note: Round off to the nearest whole number
- Volume of sphere :
where r is the radius. - Substituting values in the volume formula
- We get the volume =
cm 3 - We have found the desired answer.
Example 11: A shot-putt is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.8 g per
- Volume of shot-putt :
where r is the radius. - Substituting values in the volume formula
- We get the volume =
cm 3 - Mass =
× Volume. We can use this to find the mass. - Mass of shot-putt =
kg. (Round off to two decimal places) - We have found the desired answer.
Example 12: A hemispherical bowl has a radius of 3.5 cm. The volume of water it contains is equal to ? cm3
Note: Round off to the nearest whole number
- Volume of bowl :
where r is the radius. - Substituting values in the volume formula
- We get the volume =
cm 3 - We have found the desired answer.