What is the length of the diameter of a circle with an area of 50π cm²?

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Question: What is the length of the diameter of a circle with an area of 50π cm²?

Options:

Correct Answer: 10 cm

Solution:

Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2r = 2√50 = 10 cm.

What is the length of the diameter of a circle with an area of 50π cm²?

What is the length of the diameter of a circle with an area of 50π cm²?

Step 1: Write down the formula for the area of a circle, which is Area = πr².
Step 2: We know the area is 50π cm², so we can set up the equation: 50π = πr².
Step 3: To simplify, divide both sides of the equation by π: 50 = r².
Step 4: Now, to find the radius (r), take the square root of both sides: r = √50.
Step 5: The diameter (D) of a circle is twice the radius, so use the formula: D = 2r.
Step 6: Substitute the value of r into the diameter formula: D = 2√50.
Step 7: Simplify 2√50. Since √50 can be simplified to 5√2, we have D = 2 * 5√2 = 10√2 cm.
Step 8: If needed, you can approximate √2 to get a numerical value for the diameter.

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