Final answer:
The largest possible volume of a cylinder inscribed in a sphere with a radius of 5 meters is found using the formula V = πr²h and is approximately 785.398 cubic meters.
Step-by-step explanation:
Finding the Largest Possible Volume of an Inscribed Cylinder
To find the largest possible volume of a cylinder inscribed in a sphere with a radius of 5 meters, we need to use the formula for the volume of a cylinder, which is V = πr²h, where r is the radius of the cylinder and h is the height
Since the cylinder is inscribed in the sphere, the diameter of the cylinder is equal to the diameter of the sphere. Thus, the height of the cylinder, h, is equal to the diameter of the sphere, which is 10 meters (2 * radius of the sphere).
The radius of the base of the cylinder, r, would be the same as the radius of the sphere, which is 5 meters, because the cylinder will be at its maximum possible volume when it has the same height and diameter (this occurs when the cylinder's axis aligns with the sphere's diameter).
The largest possible volume of the cylinder can then be calculated as:
V = π * (5 m)² * 10 m
V = π * 25 m² * 10 m
V = 250π m³
V ≈ 250 * 3.14159 m³
V ≈ 785.398 m³
Therefore, the largest possible volume of the cylinder is approximately 785.398 cubic meters.