Final answer:
To find the volume of a cylinder with a height of 5cm and base circumference of 16x cm, calculate the radius using the formula C = 2πr, substitute it into the volume formula V = πr²h, and choose the closest answer from the options, resulting in 320x cm³.
Step-by-step explanation:
The volume of a cylinder is calculated using the formula V = πr²h, where V is volume, r is the radius of the base, and h is the height of the cylinder. Given that the height of the cylinder is 5 centimeters and the circumference of the base is 16x centimeters, we need to find the radius first. Since the circumference C is given by C = 2πr, solving for r gives us r = C / (2π). Substituting the given values, the radius is 16x / (2π). Therefore, the volume of the cylinder is π * (16x / (2π))² * 5, which simplifies to 40x π2 cm³. However, the answers given are not in terms of π, so we must select the closest option to the simplified term, which is 320x cm³ (Option B), assuming π is approximately 3.14.