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Chapter 0: Problem 68

In computing the dosage for chemotherapy, a patient's body surface area is needed. A good approximation of a person's surface area \(s,\) in square meters \(\left(m^{2}\right),\) is given by the formula $$s=\sqrt{\frac{h w}{3600}},$$ where w is the patient's weight in kilograms (kg) and h is the patient's height in centimeters (cm). (Source: U.S. Oncology.) Use the preceding information. Round your answers to the nearest thousandth. Assume that a patient's weight is 70 kg. Approximate the patient's surface area assuming that: a) The patients height is 150 cm. b) The patients height is 180 cm.

Short Answer

Expert verified
(a) 1.709 m^2, (b) 1.871 m^2

Step by step solution

01

- Understand the given formula

The given formula to approximate a person's surface area is \[ s = \sqrt{\frac{h \cdot w}{3600}} \]where:- \( h \) is the height in centimeters (cm)- \( w \) is the weight in kilograms (kg)- \( s \) is the surface area in square meters \( m^2 \).
02

- Input values for part (a)

For part (a), the given values are: - Weight \( w = 70 \) kg - Height \( h = 150 \) cm.Substitute these values into the formula: \[ s = \sqrt{\frac{150 \cdot 70}{3600}} \]
03

- Calculate the expression inside the square root for part (a)

First, calculate the product of height and weight:\[ 150 \times 70 = 10500 \]Next, divide by 3600:\[ \frac{10500}{3600} \approx 2.917 \]
04

- Find the square root for part (a)

Calculate the square root of the result from Step 3:\[ s = \sqrt{2.917} \approx 1.709 \]So, the surface area for part (a) is approximately \( 1.709 \: m^2 \).
05

- Input values for part (b)

For part (b), the given values are:- Weight \( w = 70 \) kg- Height \( h = 180 \) cm.Substitute these values into the formula:\[ s = \sqrt{\frac{180 \cdot 70}{3600}} \]
06

- Calculate the expression inside the square root for part (b)

First, calculate the product of height and weight:\[ 180 \times 70 = 12600 \]Next, divide by 3600:\[ \frac{12600}{3600} \approx 3.500 \]
07

- Find the square root for part (b)

Calculate the square root of the result from Step 6:\[ s = \sqrt{3.500} \approx 1.871 \]So, the surface area for part (b) is approximately \( 1.871 \: m^2 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

body surface area
In chemotherapy and other medical treatments, accurate dosage administration is crucial. One widely used method for determining the correct dosage involves calculating the patient's Body Surface Area (BSA). The BSA is a measurement of the body's external surface and is used to tailor medical treatments to individual needs.

The formula used for approximating the BSA is:
\[ s = \sqrt{\frac{h \cdot w}{3600}} \]
where:
- **\( h \)** is the height in centimeters
\( \text{(cm)}\)
- **\( w \)** is the weight in kilograms
\( \text{(kg)}\)
- **\( s \)** is the surface area in square meters
\( m^2 \).

This formula takes into account both the patient's weight and height to provide a reliable approximation of the BSA.
dosage computation
Once the BSA is known, the next step in chemotherapy involves dosage computation. This is the process of determining the exact amount of medication the patient should receive.

For chemotherapy treatments, the dosage is often expressed in milligrams per square meter \( mg/m^2 \). This means that the dose will be proportional to the patient's BSA.

The computation follows this structure:
1. **Calculate BSA**: Use the formula to find the body surface area.
2. **Determine dosage**: Multiply the BSA by the prescribed amount of medication per square meter.

For example, if a medication dosage is 50 \( mg/m^2 \) and the patient鈥檚 BSA is 1.709 \( m^2 \), the total dosage would be:

\[ 50 \cdot 1.709 = 85.45 \ mg. \]

This ensures that each patient receives a personalized dose based on their own BSA, optimizing treatment effectiveness and minimizing side effects.
chemotherapy calculations
Chemotherapy involves using medications to kill or slow the growth of cancer cells. Because the correct dosage is vital, detailed calculations are essential. Let's dive into the example given:

**Example for Part (a)**:
  • **Weight**: 70 kg
  • **Height**: 150 cm
  • Using the formula, we calculate:
  • \[ s = \sqrt{\frac{150 \cdot 70}{3600}} \approx 1.709 \ m^2 \]

**Example for Part (b)**:
  • **Weight**: 70 kg
  • **Height**: 180 cm
  • Using the formula, we calculate:
  • \

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