Problem 112 - 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 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: Identify given values

First, identify the values provided in the problem. The individual's height, \( h \), is 74 inches, and their weight, \( w \), is 225 pounds.

Step 2: Input values into the Mosteller formula

Substitute the given values into the Mosteller formula: \[ B = \sqrt{\frac{hw}{3131}} \]Substituting the values:\[ B = \sqrt{\frac{74 \times 225}{3131}} \]

Step 3: Calculate the product of height and weight

Multiply the height and weight: \( h \times w = 74 \times 225 = 16650 \).

Step 4: Divide by 3131

Now divide the product of height and weight by 3131: \( \frac{16650}{3131} \approx 5.3185 \).

Step 5: Calculate the square root

Take the square root of the result from Step 4: \( B = \sqrt{5.3185} \approx 2.306 \).

Step 6: Round the answer to 2 decimal places

Round the result from Step 5 to two decimal places: \( B \approx 2.31 \).

Key Concepts

Body Surface Area Calculation

Body surface area (BSA) is an important metric used in medicine to assess various clinical parameters, such as drug dosages and fluid levels. Mosteller's formula provides a simplified and widely used method to calculate BSA using a person's height and weight.The formula goes: \[ B = \sqrt{\frac{hw}{3131}}, \]where:

• \( B \) is the body surface area in square meters,
• \( h \) is height in inches,
• \( w \) is weight in pounds.

The importance of using the Mosteller formula arises from its practical application in clinical settings, offering healthcare professionals a quick and relatively accurate method to evaluate BSA.The process involves substituting an individual’s height and weight into the formula, computing the product of these two values, and then dividing by 3131. Finally, taking the square root gives the body surface area.

Step-by-Step Math Solution

Calculating body surface area using the Mosteller Formula requires several straightforward steps. Tackling each methodically ensures accuracy. Here's a detailed breakdown:**Step 1: Identify Values**We start by identifying the values provided in the exercise. Here, height \( h \) is 74 inches, and weight \( w \) is 225 pounds.**Step 2: Substitute Values**Substitute these values into the Mosteller equation:\[ B = \sqrt{\frac{74 \times 225}{3131}} \]**Step 3: Multiply Height and Weight**Compute the product of height and weight:\( 74 \times 225 = 16650 \).**Step 4: Division**Divide the product by 3131:\[ \frac{16650}{3131} \approx 5.3185 \].**Step 5: Square Root**Now, find the square root of this division result:\( B = \sqrt{5.3185} \approx 2.306 \).**Step 6: Round Off**Finally, round the answer to two decimal places:\( B \approx 2.31 \).

Math Practice Problem

Understanding how to approach math practice problems is vital for mastering concepts such as calculating body surface area with the Mosteller formula. When tackling these problems, follow these tips:

• Read the problem fully before beginning. Understand exactly what is asked.
• Identify and list all given values and variables. This helps in focusing the calculation steps.
• Always use correct units when substituting into the formula. Here, height should be in inches and weight in pounds.
• Break down the exercise into smaller, manageable steps. This aids in reducing mistakes.
• Double-check calculations at each stage to ensure accuracy.

By methodically addressing each component of the problem, students gain a deeper understanding and confidence in applying mathematical formulas to real-world scenarios.