Question

fill in the blank with the appropriate answer. to determine proper dosing of a medication, doctors use the formula s = √(wh/3600) to determine a patients body - surface area (s in square meters), based on their weight (w, in pounds) and height (h, in centimeters). if someones body - surface area is 4 square meters and they are 190 cm tall, how much does the person weigh to the nearest pound?

Explanation:

Step1: Rearrange the body - surface - area formula

The formula for body - surface area $s=\sqrt{\frac{wh}{3600}}$, where $s$ is the body - surface area in square meters, $w$ is the weight in kilograms, and $h$ is the height in centimeters. We know that $s = 4$ square meters and $h=190$ cm. First, square both sides of the formula to get $s^{2}=\frac{wh}{3600}$.

Step2: Solve for $w$

Rearrange the equation $s^{2}=\frac{wh}{3600}$ to isolate $w$. Multiply both sides by $3600$: $3600s^{2}=wh$. Then $w=\frac{3600s^{2}}{h}$.

Step3: Substitute the given values

Substitute $s = 4$ and $h = 190$ into the formula for $w$. $w=\frac{3600\times4^{2}}{190}=\frac{3600\times16}{190}=\frac{57600}{190}\approx303.16$ kg.

Step4: Convert kilograms to pounds

Since 1 kg is approximately 2.20462 pounds, then the weight in pounds is $w_{pounds}=303.16\times2.20462\approx668$ pounds.

Answer:

668 pounds