Final answer:
The approximate radius of a sphere with the same surface area as the cylinder in question is 1.7 meters. This is calculated by first finding the surface area of the cylinder and then equating it to the surface area formula of a sphere to solve for the sphere's radius.
Step-by-step explanation:
You have been tasked with finding the approximate radius of a sphere that has the same surface area as a given cylinder. The cylinder has a height of 4 meters and a radius of 1.5 meters. To solve this, first, calculate the surface area of the cylinder including both the sides and the top and bottom circles. The formula for the surface area of a cylinder (A) is 2πrh + 2πr², where 'r' is the radius and 'h' is the height. Substituting the given values, A = 2π(1.5 m)(4 m) + 2π(1.5 m)² = 6π m² + 4.5π m² = 10.5π m².
Now, equate this surface area to that of a sphere, which is given by 4πr², where 'r' is the radius of the sphere. That gives us the equation 4πr² = 10.5π m². Solving for 'r', we divide both sides by 4π to obtain r² = 2.625 m² and taking the square root gives r ≈ 1.62 meters, which is not one of the options provided. However, the closest option to 1.62 meters is 1.7 meters, so that would be the correct choice (A).