Problem 113 - 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 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: Identify Given Values

We are given the height of an individual, which is \( h = 66 \) inches, and the weight of the same individual, which is \( w = 135 \) pounds. We need these values to calculate the body surface area using the Mosteller formula.

Step 2: Write Down the Mosteller Formula

The formula provided for calculating the body surface area is: \[ B = \sqrt{\frac{h w}{3131}} \] where \( B \) is the body surface area in square meters, \( h \) is the height in inches, and \( w \) is the weight in pounds.

Step 3: Substitute Given Values into the Formula

Insert the given values into the formula: \[ B = \sqrt{\frac{66 \times 135}{3131}} \]. This will allow us to perform the necessary calculations to find the body surface area.

Step 4: Calculate the Product of Height and Weight

First, calculate the product of \( h \) and \( w \): \( 66 \times 135 = 8910 \). Substitute this product into the equation: \[ B = \sqrt{\frac{8910}{3131}} \].

Step 5: Divide by 3131

Divide the product of height and weight by 3131: \( \frac{8910}{3131} \approx 2.846 \). Now the formula becomes \[ B = \sqrt{2.846} \].

Step 6: Find the Square Root

Calculate the square root of \( 2.846 \): \( \sqrt{2.846} \approx 1.688 \). This result is the value of the body surface area.

Step 7: Round the Result

Round the calculated body surface area to two decimal places: \( B \approx 1.69 \) square meters.

Key Concepts

Body Surface Area Calculation

Calculating the body surface area (BSA) is essential, especially in medical fields, as it is often used to determine dosages for medication and assess health conditions. The Mosteller formula is among the widely accepted methods for calculating BSA, due to its simplicity and reliability. The formula \[ B = \sqrt{\frac{h w}{3131}} \] helps translate both an individual's height and weight into a single number representing the body surface area in square meters.

To use this formula effectively:

• Identify the individual's height, denoted as \( h \), measured in inches.
• Determine the individual's weight, denoted as \( w \), measured in pounds.

These two pieces of information feed into the Mosteller formula, providing an accurate calculation of body surface area.

A real-world example would be a person who is 66 inches tall and weighs 135 pounds. Plug these values into the formula to find the exact body surface area. The calculated BSA is crucial for healthcare professionals to make informed decisions regarding treatment plans.

Mathematical Formulas

Mathematical formulas are expressions that define relationships between different quantities. They are essential tools for solving problems across various fields. In the context of the Mosteller formula for BSA calculation, the formula simplifies and structures the relationship between height, weight, and body surface area.

Let's break down the Mosteller formula into simpler parts:

• The formula involves a square root \( \sqrt{...} \), which is required to calculate the BSA.
• The division by 3131 influences how weight and height combine to form the final BSA value, defining the unit conversion factor.
• The multiplication \( hw \) combines two linear measurements into a composite number representing combined body dimensions.

Formulas like these help us see complex interactions as manageable problems. By understanding each component's role, we can accurately plug values into a formula and predict outcomes or behaviors.

Algebraic Expressions

Algebraic expressions, such as those found in the Mosteller formula, are essential for codifying calculations into a form that can be easily manipulated and understood universally. In an algebraic expression, variables represent measurable quantities. The Mosteller formula itself is an algebraic expression where \( h \) and \( w \) are variables representing height and weight.

Here's how to work with such expressions:

• Identify each variable and determine their respective values from the problem description or real-life measurements.
• Substitute these values into the expression properly, respecting the operations laid out by the formula.
• Follow the order of operations (PEMDAS/BODMAS) to solve the expression step-by-step.

This logical flow allows us to simplify complex problems, guiding us to accurate solutions. Algebraic expressions also encourage analytical thinking, allowing one to manipulate variables flexibly to explore different scenarios or solve for unknowns. The Mosteller formula showcases how algebra enables precision in calculating something as critical as body surface area.