Final answer:
Yes, there exists a sphere that has the same surface area and volume. The radius of this sphere is 4/3 or approximately 1.333.
Step-by-step explanation:
Yes, there exists a sphere that has the same surface area and volume. This sphere is called a “isodiametric” sphere or a “round cube.”
The formula for the surface area of a sphere is Surface Area = 4πr², and the formula for the volume of a sphere is Volume = (4/3)πr³.
By equating the two formulas and solving for the radius (r), we can find the value of r for the sphere. Let's set the surface area equal to the volume: 4πr² = (4/3)πr³.
After simplification, we have 3r = 4. Dividing both sides by 3, we find that the radius of the sphere is r = 4/3 or approximately r = 1.333.