If a circle has an area of 50π cm², what is its diameter? (2020)

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Question: If a circle has an area of 50π cm², what is its diameter? (2020)

Options:

Correct Answer: 10 cm

Exam Year: 2020

Solution:

Area = πr², so r² = 50. Thus, r = √50 = 5√2 cm. Diameter = 2r = 10√2 cm ≈ 14.14 cm.

If a circle has an area of 50π cm², what is its diameter? (2020)

If a circle has an area of 50π cm², what is its diameter? (2020)

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 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, we need to find the radius (r). To do this, take the square root of both sides: 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 = 10√2 cm.
Step 7: If you want a decimal approximation, calculate 10√2, which is approximately 14.14 cm.

Area of a Circle – Understanding the formula for the area of a circle (Area = 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 and how to compute it from the radius.