Question

Calculate the BMI of a woman who is 5 feet, 3 inches tall and weighs 130 pounds, and of a man who is 5 feet, 10 inches tall and weighs 215 pounds. State whether either of these people could be classified as "overweight" or "obese."

Short answer

The woman, with a height of 1.6002 meters and weight of 58.967008 kilograms, has a BMI of 22.97. According to the standard BMI categories, she falls within the normal weight range (18.5 ≤ BMI < 24.9), so she is neither overweight nor obese. The man, with a height of 1.778 meters and weight of 97.52244 kilograms, has a BMI of 30.70. According to the standard BMI categories, he falls within the obese category (BMI ≥ 30), so he is considered obese.

Step-by-step solution

Convert height and weight to meters and kilograms

First, we need to convert height from feet and inches to meters, and weight from pounds to kilograms. 1 feet = 0.3048 meters 1 inch = 0.0254 meters 1 pound = 0.453592 kilograms For the woman: Height: 5 feet, 3 inches = (5 × 0.3048) + (3 × 0.0254) = 1.6002 meters Weight: 130 pounds = 130 × 0.453592 = 58.967008 kilograms For the man: Height: 5 feet, 10 inches = (5 × 0.3048) + (10 × 0.0254) = 1.778 meters Weight: 215 pounds = 215 × 0.453592 = 97.52244 kilograms

Calculate the BMI using the formula

Next, we'll use the BMI formula to calculate each individual's BMI. For the woman: \(BMI = \frac{weight}{height^2} = \frac{58.967008}{1.6002^2} = 22.97\) For the man: \(BMI = \frac{weight}{height^2} = \frac{97.52244}{1.778^2} = 30.70\)

Determine the BMI categories and define overweight/obese status

Now we will compare each individual's BMI against the standard BMI categories. For the woman: Her BMI is 22.97, which falls within the normal weight category (18.5 ≤ BMI < 24.9). She is neither overweight nor obese. For the man: His BMI is 30.70, which falls within the obese category (BMI ≥ 30). He is considered obese. In conclusion, the woman has a BMI of 22.97 and is considered to have a normal weight, while the man has a BMI of 30.70 and is considered obese.

Key concepts

Conversion of Units

In order to calculate Body Mass Index (BMI) accurately, it's crucial to convert height and weight into metric units: meters and kilograms. This conversion ensures uniformity in measurements, making BMI calculations consistent globally.

• 1 foot is equivalent to 0.3048 meters.
• 1 inch translates to 0.0254 meters.
• 1 pound is equal to 0.453592 kilograms.

For instance, if someone is 5 feet and 3 inches tall, you first convert the height into meters: multiply the feet (5) by 0.3048 and add the product of inches (3) and 0.0254. This calculation provides the total height in meters. Similarly, convert weight by multiplying pounds by 0.453592 to get the weight in kilograms. This conversion is a key step before using the BMI formula.

Classification of BMI

After calculating the BMI, it's important to understand what the numbers signify by categorizing them according to standard health guidelines. The BMI categories provide a quick reference to probable health status in terms of weight.

• A BMI less than 18.5 is considered underweight.
• A BMI between 18.5 and 24.9 is classified as normal weight.
• A BMI between 25 and 29.9 indicates overweight status.
• A BMI of 30 or above is classified as obese.

These categories help individuals and healthcare professionals identify potential health risks associated with being underweight, normal weight, overweight, or obese. Remember, while BMI is a useful screening tool, it does not measure body fat directly, nor does it account for muscle mass differences.

BMI Formula

The BMI formula is straightforward, calculated using a person's weight and height. The formula is:
\[ BMI = \frac{weight \text{ (kg)}}{height^2 \text{ (m)}} \]This means you divide an individual's weight in kilograms by the square of their height in meters. This calculation provides a numerical value that can be used to quickly assess whether an individual's weight falls within a healthy range.
For example, if someone weighs 58.967 kilograms and is 1.6002 meters tall, their BMI is computed as follows:
\[ BMI = \frac{58.967}{1.6002^2} \approx 22.97 \]This example illustrates how the formula gives you a specific number that can then be referenced within the standard BMI classification to understand one's weight status. Be mindful that while BMI is widely used, it might not always provide a complete picture of an individual's health.