Question

The surface area of animals and humans can be calculated using the formula: S = km⅔, where m = mass in grams and k = a constant, and S = cm2. Approximate the surface area of a child with a k value of 10 and a mass of 5 kilograms.

Answer 1

To calculate the surface area of a child with a mass of 5 kg and a constant k of 10, convert the mass to grams, calculate the mass to the power of 2/3, and then multiply by the constant to get the surface area in cm2. The approximate surface area is 21793 cm2.

Step-by-step explanation:

To calculate the surface area of a child given a mass (m) of 5 kilograms using the formula S = km⅔, where k is a constant with a value of 10, follow these steps:

1. Convert the mass from kilograms to grams, because the formula requires mass in grams (m = 5000 grams).
2. Calculate the mass to the power of 2/3 (m⅔ = 5000⅔).
3. Finally, calculate the surface area by multiplying the constant (k = 10) with the result from step 2 (S = 10 × 5000⅔ cm2).

Now, implement the actual math:

m⅔ = 5000⅔ = (5 × 103)⅔ ≈ 2179.3 grams⅔

S = 10 × 2179.3 cm2 ≈ 21793 cm2

Therefore, the approximate surface area of the child is 21793 cm2.