What is the diameter of a circle with an area of 78.5 cm²? (2018)

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Question: What is the diameter of a circle with an area of 78.5 cm²? (2018)

Options:

Correct Answer: 10 cm

Exam Year: 2018

Solution:

Area = πr²; 78.5 = πr²; r² = 78.5/π; d = 2√(78.5/π) ≈ 10 cm.

What is the diameter of a circle with an area of 78.5 cm²? (2018)

What is the diameter of a circle with an area of 78.5 cm²? (2018)

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 78.5 cm², so we can set up the equation: 78.5 = πr².
Step 3: To find r², we need to isolate it. Divide both sides by π: r² = 78.5 / π.
Step 4: Now, we need to find the radius r. To do this, take the square root of r²: r = √(78.5 / π).
Step 5: The diameter d of the circle is twice the radius, so we use the formula: d = 2r.
Step 6: Substitute r into the diameter formula: d = 2√(78.5 / π).
Step 7: Finally, calculate the value using π (approximately 3.14) to find the diameter: d ≈ 10 cm.

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