Answer:
The ratio of the volume of one sphere to the volume of the right cylinder is 1 : 3 ⇒ answer B
Step-by-step explanation:
* Lets explain how to solve the problem
- The spheres touch the two bases of the cylinder
∴ The height of the cylinder = the diameters of the two spheres
∵ The diameter of the sphere = twice its radius
∴ The diameter of the sphere = 2r, where r is the radius of the sphere
∵ The height of the cylinder = 2 × diameter of the sphere
∴ The height of the cylinder = 2 × 2r = 4r
- The spheres touch the curved surface of the cylinder, that means
the diameter of the sphere equal the diameter of the cylinder
∴ The maximum possible radius of the sphere is the radius of the
cylinder
∵ The radius of the sphere is r
∴ The radius of the cylinder is r
- The volume of the cylinder is πr²h and the volume of the sphere is
4/3 πr³
∵ The height of the cylinder = 4r ⇒ proved up
∵ The radius of the cylinder = r
∵ The volume of the cylinder = πr²h
∴ The volume of the cylinder = πr²(4r) = 4πr³
∵ The radius of the sphere = r
∵ The volume of the sphere = 4/3 πr³
∴ The ratio of the volume of one sphere to the volume of the right
cylinder = 4/3 πr³ : 4 πr³
- Divide both terms of the ratio by 4 πr³
∴ The ratio = 1/3 : 1
- Multiply both terms of the ratio by 3
∴ The ratio = 1 : 3
∴ The ratio of the volume of one sphere to the volume of the right
cylinder is 1 : 3
