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In Mathematics / College | 2025-07-07

What is a circle's diameter if its area is 25π square inches?
A. 5 inches
B. 10 inches
C. 25 inches
D. 50 inches

Asked by ktoney171

Answer (2)

The area of the circle is 25 π .
Use the formula for the area of a circle A = π r 2 to find the radius.
Substitute the given area into the formula and solve for r : 25 π = π r 2 , so r = 5 inches.
Calculate the diameter using d = 2 r , so d = 2 ( 5 ) = 10 inches. The final answer is 10 in c h es ​ .

Explanation

Problem Analysis We are given that the area of the circle is 25 π square inches. We need to find the diameter of the circle.

Area of a Circle Formula The area of a circle is given by the formula: A = π r 2 where A is the area and r is the radius of the circle.

Substitute the Given Area We are given A = 25 π . Substituting this into the formula, we get: 25 π = π r 2

Solve for the Radius Dividing both sides of the equation by π , we have: r 2 = 25 Taking the square root of both sides, we get: r = 25 ​ = 5 So, the radius of the circle is 5 inches.

Calculate the Diameter The diameter of a circle is twice its radius, so: d = 2 r Substituting r = 5 inches, we get: d = 2 ( 5 ) = 10 Therefore, the diameter of the circle is 10 inches.

Final Answer The diameter of the circle is 10 inches, which corresponds to option B.


Examples
Understanding the area and diameter of circles 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. Knowing the diameter helps you plan the layout and spacing of elements within the garden, ensuring a harmonious and efficient design. Similarly, in engineering, calculating the area and diameter of circular pipes is essential for determining flow rates and structural integrity.

Answered by GinnyAnswer | 2025-07-07

The diameter of the circle is 10 inches, which corresponds to option B.
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Answered by Anonymous | 2025-07-24

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