A circle has an area of 50.24 cm². What is its diameter?

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Question: A circle has an area of 50.24 cm². What is its diameter?

Options:

Correct Answer: 10 cm

Solution:

Area = πr², so r = √(Area/π) = √(50.24/π) ≈ 4 cm. Diameter = 2r = 8 cm.

A circle has an area of 50.24 cm². What is its diameter?

A circle has an area of 50.24 cm². What is its diameter?

Step 1: Understand that the area of a circle is given by the formula Area = πr², where r is the radius.
Step 2: We know the area of the circle is 50.24 cm².
Step 3: To find the radius (r), we need to rearrange the formula: r = √(Area/π).
Step 4: Substitute the area into the formula: r = √(50.24/π).
Step 5: Calculate π (approximately 3.14) and divide: 50.24/π ≈ 16.00.
Step 6: Now find the square root: r = √(16.00) = 4 cm.
Step 7: The diameter (d) of the circle is twice the radius: d = 2r = 2 * 4 cm = 8 cm.

Area of a Circle – The area of a circle is calculated using the formula A = πr², where r is the radius.
Radius and Diameter Relationship – The diameter of a circle is twice the radius, expressed as d = 2r.
Square Root Calculation – Finding the radius involves taking the square root of the area divided by π.