Problem 114 - Intermediate Algebra

Question

The Mosteller formula for calculating adult body surface area is \(B=\sqrt{\frac{h w}{3131}},\) where \(B\) is an individual's body surface area in square meters, \(h\) is the individual's height in inches, and \(w\) is the individual's weight in pounds. Use this information to answer Exercises 113 and 114 . Round answers to 2 decimal places. Find the body surface area of an individual who is 74 inches tall and who weighs 225 pounds.

Step-by-Step Solution

Answer

The body surface area is approximately 2.31 square meters.

Step 1: Substitute Values into Formula

Start by identifying the values for height and weight. Here, height \(h = 74\) inches and weight \(w = 225\) pounds. Substitute these values into the Mosteller formula for body surface area: \( B = \sqrt{\frac{hw}{3131}} \).

Step 2: Calculate the Product of Height and Weight

Multiply the height \(h\) by the weight \(w\). \(74 \times 225 = 16650\). This yields \(hw = 16650\).

Step 3: Divide by 3131

Divide the product obtained by 3131. \(\frac{16650}{3131} \approx 5.3181\).

Step 4: Take the Square Root

Find the square root of the result from the previous step. \(B = \sqrt{5.3181} \approx 2.30653\).

Step 5: Round to Two Decimal Places

Round the final answer to two decimal places to obtain the body surface area. Therefore, \(B \approx 2.31\) square meters.

Key Concepts

Body Surface Area Calculation

Calculating body surface area (BSA) is an essential aspect in medical settings to determine appropriate drug dosages and assess cardiac output. The Mosteller formula is one of the common methods for estimating the BSA and is appreciated for its simplicity. This specific formula is expressed as:\[ B = \sqrt{\frac{hw}{3131}} \]where:

• B is the body surface area in square meters.
• h represents the individual’s height in inches.
• w stands for the weight in pounds.

To find the BSA using this formula, follow these steps: first, plug in the known values for height and weight. Next, calculate their product, divide by the given constant 3131, and finally, take the square root of the result. The ability to interpret and calculate BSA is especially crucial for healthcare providers to personalize medical care.

Rounding Decimals

Rounding decimals involves approximating a number to a specific number of decimal places for simplicity or alignment with precision levels required in calculations. In the context of our exercise, rounding is crucial in conveying the body surface area to two decimal places for clarity and accuracy in medical records. Steps for rounding include:

• Identify the decimal place to which you’ll round. In this case, it is the second decimal place.
• Look at the digit immediately following it. If it is 5 or greater, round up the target digit.
• If the next digit is less than 5, retain the target digit as is.

For instance, the calculated BSA before rounding was approximately 2.30653. Since the third decimal (6) is greater than 5, the second decimal place (0) is rounded up to 1, finalizing the result to 2.31 square meters. Understanding decimal rounding ensures precision and consistency across scientific and mathematical calculations.

Multiplying and Dividing Steps

In the process of applying the Mosteller formula, multiplication and division are fundamental operations needed to arrive at the correct estimation of body surface area. These steps involve handling and simplifying expressions that may initially seem complex.

• Begin by multiplying the height by the weight. For example, with h = 74 inches and w = 225 pounds, the multiplication yields 16650: \( 74 \times 225 = 16650 \)
• Follow this by dividing the product by 3131, a constant specific to the Mosteller formula. This operation is essential to adjust the measurements into a unit suitable for square meter calculations. Thus, \( \frac{16650}{3131} \approx 5.3181 \)

Performing these two basic mathematical operations with attention to detail helps maintain the precision necessary for accurate BSA calculation. Mastering such steps reinforces arithmetic skills critical for academic and practical applications.