Problem 111 - Algebra A Combined Function

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 111 and 112. Round answers to 2 decimal places. Find the body surface area of an individual who is 66 inches tall and who weighs 135 pounds.

Step-by-Step Solution

Answer

The body surface area is approximately 1.69 square meters.

Step 1: Understanding the Problem

We need to calculate the body surface area (BSA) using the Mosteller formula: \(B = \sqrt{\frac{h w}{3131}}\). In this problem, the height \(h\) is 66 inches and the weight \(w\) is 135 pounds. We are required to find the BSA and round the result to 2 decimal places.

Step 2: Substitute Values

Substitute the given values into the Mosteller formula: \[ B = \sqrt{\frac{66 \times 135}{3131}} \].

Step 3: Calculate the Intermediate Step

First, multiply the height by the weight: \(66 \times 135 = 8910\). Then, substitute this into the formula: \[B = \sqrt{\frac{8910}{3131}}\].

Step 4: Division

Divide 8910 by 3131: \(\frac{8910}{3131} \approx 2.8451\).

Step 5: Square Root and Round

Take the square root of 2.8451: \(\sqrt{2.8451} \approx 1.687\). Round 1.687 to 2 decimal places to get 1.69. Thus, the body surface area is approximately 1.69 square meters.

Key Concepts

Body Surface Area

Body surface area (BSA) is a measurement that represents the total surface area of a person's body. It is often used in medical fields to help determine dosages for medications and to assess a person's nutritional needs. Calculating BSA provides a more accurate metric than just using weight or height alone.The Mosteller formula is a widely used equation for estimating BSA. The formula is \[ B = \sqrt{\frac{h w}{3131}} \]where \(B\) is the body surface area in square meters, \(h\) is height in inches, and \(w\) is weight in pounds. This formula simplifies the calculation by incorporating both height and weight into a single operation. It's easy to use and provides results rounded to practical decimal places, typically two, for precision in medical settings.

Height and Weight Conversion

In the Mosteller formula for BSA, height is measured in inches and weight in pounds. These are common units in the United States. However, understanding how to convert these measurements is essential when comparing data or using formulas from other systems, such as metric calculations.

• To convert height from inches to centimeters, multiply by 2.54.
• To convert weight from pounds to kilograms, divide by 2.205.

Converting units might be necessary in situations such as medical research or when utilizing medical data from different countries. Being familiar with metric conversions ensures that data integrity is maintained across various systems.

Metric Calculations

Metric calculations often provide a universal standard due to their global usage. They simplify scientific and medical data analyses by using units like kilograms for weight and meters for height. In many health assessments, such as calculating body mass index (BMI) or drug dosages, the metric system is preferred for its precision. When using formulas like Mosteller's to determine BSA, ensure that the original units are specified to avoid confusion. For Mosteller's specific formula, the need to use inches and pounds is explicit in the formula's structure. Still, knowing metric equivalents can aid in confirming accuracy and understanding alternative methods used in international contexts.

Square Root Calculation

The square root calculation is the final step in the Mosteller formula. It is a mathematical operation that determines a number which, when multiplied by itself, yields the original number.In the formula \( B = \sqrt{\frac{h w}{3131}} \), after computing the division, the square root operation refines the result to give the BSA in square meters. Tools like calculators or mathematical software are typically used for precise square root calculations, especially when dealing with decimals.Rounding is often required after calculating square roots to ensure that the final value is practical, particularly in medical settings where exact numbers could affect treatment outcomes. Therefore, understanding how to perform square root operations and accurately round the results is crucial for these applications.