Show, by means of calculations, that a cow with a girth of 70 inches and a body length of 78 inches has a weight of [tex]$577,88 kg$[/tex].
You may use the formula:
Animal weight in pounds [tex]$=\frac{(\text { girth })^2 \times \text { body length }}{300}$[/tex]
Note: [tex]$1 kg=2,2046$[/tex] pounds
Answer (2)
Calculate the weight in pounds: 300 7 0 2 × 78 = 1274 pounds.
Convert the weight to kilograms: 2.2046 1274 = 577.88 kg.
Compare the calculated weight with the given weight.
The calculated weight matches the given weight, so the answer is 577.88 k g .
Explanation
Problem Analysis We are given the formula to calculate the weight of an animal in pounds based on its girth and body length. We are also given a conversion factor to convert pounds to kilograms. Our goal is to verify that a cow with a girth of 70 inches and a body length of 78 inches has a weight of 577.88 kg.
Calculating Weight in Pounds First, we calculate the weight of the cow in pounds using the given formula: Animal weight in pounds = 300 ( girth ) 2 × body length Substituting the given values, we have: Animal weight in pounds = 300 ( 70 ) 2 × 78 Animal weight in pounds = 300 4900 × 78 Animal weight in pounds = 300 382200 Animal weight in pounds = 1274 So, the weight of the cow is 1274 pounds.
Converting Pounds to Kilograms Next, we convert the weight from pounds to kilograms using the given conversion factor: 1 kg = 2.2046 pounds Weight in kg = 2.2046 Weight in pounds Weight in kg = 2.2046 1274 Weight in kg = 577.8826090900843 So, the weight of the cow is approximately 577.88 kg.
Verification Finally, we compare the calculated weight in kilograms with the target weight of 577.88 kg. Since the calculated weight (577.88 kg) is approximately equal to the target weight (577.88 kg), the statement is verified.
Conclusion Therefore, a cow with a girth of 70 inches and a body length of 78 inches has a weight of approximately 577.88 kg, as shown by our calculations.
Examples
Understanding how to estimate an animal's weight using simple measurements like girth and body length can be incredibly useful in farming and veterinary science. For instance, farmers can use these estimations to determine the correct dosage of medication for their livestock, ensuring the health and well-being of the animals. Veterinarians can also use these estimations during field visits when scales are not available, providing quick and accurate assessments of an animal's condition. This method provides a practical way to manage and care for animals effectively.
Using the given formula, the weight of the cow was calculated to be 1274 pounds. After converting this weight to kilograms using the conversion factor, the result was approximately 577.88 kg, confirming the original statement. Therefore, the cow's weight is accurately represented as 577.88 kg.
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