The diameter of a solid metallic right circular cylinder is equal to its height. After cutting out the largest possible solid sphere S from the cylinder, the remaining material is recast to form a solid sphere S1. What is the ratio of the radius of the sphere S to that of sphere S1?
Answer:
3√2:1
- Given, the diameter of the cylinder = height of the cylinder
We need to know the formula for calculating the volume of a cylinder and the volume of a sphere for this question. - The volume of a cylinder with radius and height
Volume of the given cylinder - The radius sphere
The volume of the sphere
Therefore, the volume of the remaining material - The remaining material is recast to form a solid sphere
Let the radius of
The volume of
- Therefore, the required ratio is