Final answer:
The inside radius of a coffee mug holding 375 g of coffee with the density similar to water and filled to a depth of 5.5 cm is calculated using the volume formula for a cylinder, yielding an approximate radius of 3.484 cm.
Step-by-step explanation:
To find the inside radius of a coffee mug with a given mass of coffee and density equivalent to water, we use the formula for the volume of a cylinder, V = πr²h, where V stands for volume, r for radius, and h for height. Given that the density of water is 1.00 g/cm³ (which is the same as the density of the coffee), we can say that the volume of coffee is also 375 cm³ because mass equals density times volume (m = ρV). The height (h) of the coffee in the cup is 5.5 cm. Thus, rearranging the volume formula to solve for radius (r), we have:
r = √(V / (πh))
Plugging in the values, we get:
r = √(375 cm³ / (3.14 × 5.5 cm))
Calculating this gives us the inside radius,
Radius = 3.484 cm (approximately).
This radius is the measure we seek for the coffee mug's dimension.