What is the length of the diameter of a circle with an area of 50π square units?

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Question: What is the length of the diameter of a circle with an area of 50π square units? (2023)

Options:

Correct Answer: 10 units

Exam Year: 2023

Solution:

Area = πr². Given area = 50π, r² = 50, r = √50 = 5√2. Diameter = 2r = 10√2 units.

What is the length of the diameter of a circle with an area of 50π square units? (2023)

What is the length of the diameter of a circle with an area of 50π square units? (2023)

Step 1: Recall the formula for the area of a circle, which is Area = πr², where r is the radius.
Step 2: We know the area of the circle is 50π square units. So we can set up the equation: πr² = 50π.
Step 3: To simplify, divide both sides of the equation by π. This gives us r² = 50.
Step 4: Now, to find the radius (r), take the square root of both sides: r = √50.
Step 5: Simplify √50. This can be written as √(25 * 2) = √25 * √2 = 5√2.
Step 6: The diameter (d) of a circle is twice the radius. So, d = 2r = 2 * (5√2) = 10√2.
Step 7: Therefore, the length of the diameter is 10√2 units.

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