If the area of a circle is 50π cm², what is the diameter? (2022)

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Question: If the area of a circle is 50π cm², what is the diameter? (2022)

Options:

Correct Answer: 20 cm

Exam Year: 2022

Solution:

Area = πr² = 50π. Thus, r² = 50, r = √50 = 5√2 cm. Diameter = 2r = 10√2 cm ≈ 20 cm.

If the area of a circle is 50π cm², what is the diameter? (2022)

If the area of a circle is 50π cm², what is the diameter? (2022)

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 is 50π cm². 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), we need to take the square root of both sides. So, r = √50.
Step 5: Simplify √50. This can be written as √(25 * 2) = √25 * √2 = 5√2 cm.
Step 6: The diameter (d) of a circle is twice the radius. So, d = 2r = 2 * 5√2 cm.
Step 7: Calculate the diameter: d = 10√2 cm.
Step 8: If needed, you can approximate 10√2. Since √2 is about 1.414, then 10√2 is approximately 10 * 1.414 = 14.14 cm.

Area of a Circle – Understanding the formula for the area of a circle (A = πr²) and how to manipulate it to find the radius and diameter.
Square Roots – Calculating square roots and understanding their implications in geometry.
Diameter Calculation – Knowing that the diameter is twice the radius (d = 2r) and how to apply this in problem-solving.