Find The Area Of A Circle With A Diameter Of 16 Inches. Use 3.14 For Pi.a.50.24 In2b.100.48 In2c.200.96

Find The Area Of A Circle With A Diameter Of 16 Inches. Use 3.14 For Pi.a.50.24 In2b.100.48 In2c.200.96

Understanding how to find the area of a circle is a fundamental skill in geometry, applicable in various fields such as engineering, design, and everyday problem-solving. When given the diameter of a circle, calculating its area involves a straightforward process, especially when using an approximate value for Pi, like 3.14. In this article, we will focus on finding the area of a circle with a diameter of 16 inches, illustrating the calculation process and providing useful insights. We will also explore how the options a.50.24 in², b.100.48 in², and c.200.96 in² relate to the problem, helping you understand which answer is correct and why.

Understanding the Basics: Diameter, Radius, and Area of a Circle

What Is the Diameter of a Circle?

The diameter of a circle is the longest distance across the circle, passing through its center. It measures the full width of the circle and is crucial in calculating the area because it relates directly to the radius.

Relationship Between Diameter and Radius

The radius of a circle is half of its diameter:

• Radius (r) = Diameter / 2

For our example, where the diameter is 16 inches:

• r = 16 inches / 2 = 8 inches

Formula for the Area of a Circle

The area (A) of a circle can be calculated using the formula:

• A = π × r²

Where:

• π (Pi) is approximately 3.14 in this context
• r is the radius of the circle

Calculating the Area of the Circle

Step-by-Step Calculation

Using the formula A = π × r²:

• Identify the radius: r = 8 inches
• Use the given approximation for Pi: π = 3.14
• Calculate r²: 8 × 8 = 64
• Multiply by Pi: 3.14 × 64 = 200.96

Therefore, the area of the circle is 200.96 square inches.

Final Result

The area of the circle with a diameter of 16 inches, using 3.14 for Pi, is:

• 200.96 in²

This matches option c.200.96 in² from the provided choices.

Understanding the Multiple-Choice Options

Option a. 50.24 in²

This value is significantly smaller than the actual area calculated. It might result from a miscalculation or using a different radius.

Option b. 100.48 in²

This is approximately half of the correct area, suggesting perhaps a mistake in the radius or the formula application.

Option c. 200.96 in²

This is the correct area based on the calculation using the specified diameter and Pi approximation.

Additional Tips for Calculating Circle Areas

Use of Pi Approximations

While 3.14 is commonly used for Pi, more precise calculations often use 3.1416 or more decimal points to increase accuracy, especially in professional contexts.

Confirming Calculations

Always double-check your calculations:

• Verify the radius: ensure it's half of the diameter
• Use consistent units throughout
• Recalculate the multiplication to avoid errors

Practical Applications

Knowing how to find the area of a circle is useful in:

• Designing circular objects like tables or wheels
• Calculating material requirements for circular surfaces
• Understanding spatial measurements in various industries

Summary

To find the area of a circle with a diameter of 16 inches:

• Calculate the radius: 8 inches
• Apply the formula A = π × r²
• Using 3.14 for Pi: A = 3.14 × 8² = 3.14 × 64 = 200.96 in²

This confirms that the correct answer from the options provided is c.200.96 in².

Conclusion

Understanding how to find the area of a circle with a given diameter is a fundamental mathematical skill. By knowing the relationship between diameter, radius, and area, and applying the correct formula with an appropriate value for Pi, you can quickly determine the area of any circle. In this case, with a diameter of 16 inches and Pi approximated as 3.14, the area is 200.96 square inches, matching option c. Recognizing these calculations and options aids in solving practical problems efficiently and accurately.