Empirical data suggest thatthe surface area of a 180-cm-tall human body changes at the rate ofsquare meters/kilogram, where W is the weight of the body inkilograms. If the surface area of a 180-cm-tall human body weighing 70 kg is 1.886277 m ,what is the surface area of a human body of the same height weighing 75 kg?
To find the surface area of a human body weighing 75 kg, we can use the empirical data provided. We are given that the surface area of a 180-cm-tall human body weighing 70 kg is 1.886277 m².
Let's break down the problem step by step:
Step 1: Identify the known values:
- Height of the human body: 180 cm
- Weight of the human body: 70 kg
- Surface area of the 70 kg body (given): 1.886277 m²
Step 2: Calculate the surface area per kilogram:
We're told that the surface area changes at a rate of square meters/kilogram. So, we need to determine the rate of change.
To do this, we'll divide the surface area (1.886277 m²) by the weight (70 kg):
Surface area per kilogram = 1.886277 m² / 70 kg
Step 3: Calculate the surface area of the 75 kg body:
Now that we know the surface area per kilogram, we can calculate the surface area of the 75 kg body. We'll multiply the surface area per kilogram by the weight of the body.
Surface area of 75 kg body = Surface area per kilogram * 75 kg
Let's plug in the values:
Surface area per kilogram = 1.886277 m² / 70 kg ≈ 0.02694681 m²/kg
Surface area of 75 kg body = 0.02694681 m²/kg * 75 kg ≈ 2.02101075 m²
Therefore, the surface area of a human body of the same height (180 cm) weighing 75 kg is approximately 2.02101075 m².