Final answer:
The minimum height the different mug must be to prevent overflow is 2.2 inches.
Step-by-step explanation:
To determine the minimum height the different mug must be – so it does not overflow when Melody pours the water into it from her original mug – we need to calculate the volume of water in her original mug and compare it to the volume of the different mug.
The volume of a cylinder can be calculated using the formula V = Πr2h, where V is the volume, Π is approximately 3.14, r is the radius, and h is the height.
The radius of Melody's original mug is half the diameter, which is 3.5 / 2 = 1.75 inches. Using the volume formula, we have V = 3.14 × (1.75)2 × 4 = 48.495 cubic inches. To find the minimum height for the different mug, we can rearrange the volume formula to solve for h: h = V / (Πr2).
Plugging in the values, we get h = 48.495 / (3.14 × (1.5)2) = 2.181 inches. Rounded to the nearest tenth, the minimum height the different mug must be is 2.2 inches.