Asphere and a cylinder have the same radius and height the volume of the cylinder is 18cm3 what is the volume

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

step-by-step explanation:

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it would take 7/10 of an hour too fill the pool.

step-by-step explanation: