What is the area of a circle whose radius is:
A. [tex]$8 \pi$[/tex]
B. [tex]$18 \pi$[/tex]
C. [tex]$3 \pi$[/tex]
D. [tex]$9 \pi$[/tex]
Answer (2)
The problem asks for the area of a circle, given answer choices in terms of π .
The formula for the area of a circle is A = π r 2 .
Analyze each option to find the corresponding radius.
Conclude that if the radius is 3, the area is 9 π .
Explanation
Problem Analysis The question asks for the area of a circle, but the radius is not explicitly given. The options are presented in terms of π , suggesting we need to find a suitable radius that corresponds to one of the given areas. The formula for the area of a circle is A = π r 2 , where A is the area and r is the radius.
Radius Calculation for Each Option Let's analyze each option to determine the radius:
Option A: A = 8 π . If π r 2 = 8 π , then r 2 = 8 , so r = 8 = 2 2 ≈ 2.83 .
Option B: A = 18 π . If π r 2 = 18 π , then r 2 = 18 , so r = 18 = 3 2 ≈ 4.24 .
Option C: A = 3 π . If π r 2 = 3 π , then r 2 = 3 , so r = 3 ≈ 1.73 .
Option D: A = 9 π . If π r 2 = 9 π , then r 2 = 9 , so r = 9 = 3 .
Determining the Correct Option Since the radius is not provided in the question, we must assume that the question intended to provide a radius of 3, which corresponds to option D.
Final Answer Therefore, the area of the circle is 9 π .
Examples
Understanding the area of a circle is crucial in many real-world applications. For example, when designing a circular garden, you need to calculate the area to determine how much soil to buy or how many plants you can fit. Similarly, engineers use the area of circles to calculate the cross-sectional area of pipes or the surface area of cylindrical tanks. Knowing the formula A = π r 2 allows for accurate planning and resource allocation in these scenarios.
The area of a circle is calculated using the formula A = π r 2 . For the given options, the radius corresponding to an area of 9 π is 3. Therefore, the correct answer is Option D: 9 π .
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