Final answer:
The cylinder with a volume of 200π cm³ has dimensions of a 5 cm radius and an 8 cm height, which is solved using the volume formula V = πr²h.
Step-by-step explanation:
The volume of a cylinder is given by the formula V = πr²h, where V is volume, r is radius, and h is height. Given the volume of the cylinder as 200π cm³, and the height being 3 cm more than the radius, we can set up the equation 200π = πr²(h), and h = r + 3. Simplify this to 200 = r²(r + 3).
We then solve the cubic equation. The correct dimensions that satisfy this equation are a radius of 5 cm and a height of 8 cm (since 5²(5 + 3) = 200). Thus, we find that with a radius of 5 cm and a height of 8 cm, the given volume of the cylinder is achieved. Option (b) is the correct answer.