Answer:
The volume of the sphere is 24 cm³
Step-by-step explanation:
* Lets explain the difference between the cylinder and the sphere
- The cylinder has two circular bases and a curved surface
- The bases of the cylinder have radius r and the curved surface has
a height h
- The volume of the cylinder = area of its base × its height
∵ The area of the circle is πr²
∴ The volume of the cylinder is V = π r² h
- A sphere is a perfectly round geometrical object in three-dimensional
space
- It the set of points that are all at the same distance r from a given point
that means its radius equals its height
- The volume of the sphere = 4/3 π r³
* Now lets solve the problem
∵ The cylinder and the sphere have the same radius and height
∵ The volume of the cylinder is 18 cm³
- Lets equate the rule of the volume of the cylinder by 18
∵ The volume of the cylinder = π r² h
∴ π r² h = 18 ⇒ divide both side by π
∴ r² h = 18/π
- The sphere and the cylinder have the same radius and height
∴ The radius and height of the sphere have the same value of the
cylinder
∵ The the height of the sphere is its radius
∴ r²h of the cylinder = r³ in the sphere
∴ r³ = 18/π
- Substitute this value in the rule of the volume of the sphere
∵ The volume of the sphere = 4/3 π r³
∴ The volume of the sphere = 4/3 π (18/π) ⇒ cancel π's
∴ The volume of the sphere = 4/3 (18) = 24 cm³
* The volume of the sphere is 24 cm³
