If the area of a circle is 78.5 cm², what is the radius? (2021)

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Question: If the area of a circle is 78.5 cm², what is the radius? (2021)

Options:

Correct Answer: 7 cm

Exam Year: 2021

Solution:

Area = πr²; 78.5 = π * r²; r² = 78.5/π = 25; r = 5 cm.

If the area of a circle is 78.5 cm², what is the radius? (2021)

If the area of a circle is 78.5 cm², what is the radius? (2021)

Step 1: Write down the formula for the area of a circle, which is Area = πr².
Step 2: Substitute the given area (78.5 cm²) into the formula: 78.5 = π * r².
Step 3: To isolate r², divide both sides of the equation by π: r² = 78.5 / π.
Step 4: Calculate the value of 78.5 / π using a calculator. This gives you r² = 25.
Step 5: To find the radius (r), take the square root of r²: r = √25.
Step 6: Calculate the square root of 25, which is 5. Therefore, the radius is 5 cm.

Area of a Circle – The area of a circle is calculated using the formula A = πr², where A is the area and r is the radius.
Algebraic Manipulation – The ability to rearrange equations to isolate variables, such as solving for r in the area formula.
Understanding of π – Recognizing that π is a constant approximately equal to 3.14, which is essential for calculations involving circles.