Final answer:
To find the radius of a cylinder with the same height and volume as a rectangular prism, we can use the formula for the volume of a cylinder. By plugging in the given values, we find that the radius is approximately 3.95 mm.
Step-by-step explanation:
To find the radius of a cylinder with the same height and volume as a rectangular prism, we need to calculate the volume of the cylinder first. The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height. We already know the height is 10 mm, and the volume of the prism is 490 mm³. Plugging these values into the formula, we can solve for r:
490 = πr²(10)
49 = πr²
r² = 49/π
r ≈ √(49/π) ≈ 3.95 mm