Question

Using the formula method for calculating BSA, determine the BSA in the following clients, and express answers to the nearest hundredth. An adult who weighs \(60.9 \mathrm{~kg}\) and is \(130 \mathrm{~cm}\) tall

Short answer

The BSA is 1.48 m².

Step-by-step solution

Define the Formula

The formula used to calculate the Body Surface Area (BSA) is the Mosteller formula: \( BSA = \sqrt{\frac{height \times weight}{3600}} \) where height is in cm and weight is in kg.

Substitute the Values

Substitute the given values into the formula: height = 130 cm and weight = 60.9 kg, so we have: \( BSA = \sqrt{\frac{130 \times 60.9}{3600}} \).

Calculate the BSA

Calculate the multiplication of height and weight: \( 130 \times 60.9 = 7917 \). Next, divide by 3600: \( \frac{7917}{3600} = 2.1991667 \). Finally, take the square root: \( \sqrt{2.1991667} \approx 1.4830 \).

Round to the Nearest Hundredth

Round the calculated BSA to the nearest hundredth: 1.4830 rounds to 1.48.

Key concepts

Mosteller formula

The Mosteller formula is a widely accepted method for calculating Body Surface Area (BSA). This formula is especially valued for its simplicity and accuracy when it comes to medical and clinical practices. BSA is an important measurement used to determine certain drug dosages, medical indicators, and physiological functions. Understanding how to calculate BSA using the Mosteller formula can be very helpful in a healthcare setting.
The formula itself is expressed as:

• \[BSA = \sqrt{\frac{height \times weight}{3600}}\]

Here, the height is input in centimeters, and the weight in kilograms. This formula relates the two dimensions to provide an estimate of the body's surface area in square meters.

step-by-step mathematical solutions

Sometimes, the easiest way to grasp a formula is through a clear, orderly calculation process. Let's walk through the calculation using the Mosteller formula, step by step:

• First, identify the necessary variables: weight = 60.9 kg and height = 130 cm.
• In Step 1, plug these values into the formula: \( BSA = \sqrt{\frac{130 \times 60.9}{3600}} \).
• Next, perform the multiplication: \( 130 \times 60.9 = 7917 \).
• Then, divide by 3600 to normalize the height-weight product: \( \frac{7917}{3600} = 2.1991667 \).
• Finally, calculate the square root of the result to find the BSA: \( \sqrt{2.1991667} \approx 1.4830 \).

By following this logical sequence, you can more clearly see how each mathematical operation builds upon the last. This clarity helps prevent mistakes and enhances your understanding of the process.

BSA rounding rules

In mathematics, rounding can significantly impact the precision and communication of results. When calculating Body Surface Area, it's essential to consider the context and application to decide on the appropriate level of precision. For BSA calculations, the standard practice is to round the result to the nearest hundredth. This precision level is usually sufficient for clinical and practical applications.
Let's look at our previously calculated example:

• The calculated BSA was approximately 1.4830.
• Rounding to the nearest hundredth involves examining the thousandth place value. Here, it is '3'.
• Since '3' is less than '5', it suggests that our number does not need to increase, so we round down to 1.48.

The rule of thumb in rounding is to increase the last digit kept if the next digit is 5 or greater, ensuring the most precise representation needed for its use.