Final answer:
To find the cylinder's height from its surface area and radius, subtract the area of both bases from the total surface area and then divide by 2πr, resulting in the formula h = (A - 2πr²) / (2πr). The provided options did not correctly represent this formula, suggesting a typo in the question.
Step-by-step explanation:
Jack wants to find the cylinder's height given the surface area and the radius. To derive the height (h) from the surface area (A) and the radius (r), we must manipulate the surface area formula of the cylinder, A = 2πrh + 2πr², where the first term represents the lateral surface area and the second term represents the area of the two circular bases. To isolate h, we first subtract the area of the bases from the total surface area, and then divide by the product of 2πr. This gives us the formula h = (A - 2πr²) / (2πr). The other options provided, such as h = 24 or h = 25, are not derived from any algebraic manipulation, so we can discount them. Thus, the correct formula to find the cylinder's height in terms of the surface area and radius is h = (A - 2πr²) / (2πr), which is not explicitly listed in the provided options, indicating a potential typo or mistake in the question.