A circle is inscribed in a square with a side length of 10 cm. What is the area

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Question: A circle is inscribed in a square with a side length of 10 cm. What is the area of the circle?

Options:

Correct Answer: 78.5 cm²

Solution:

Radius of the circle = side length / 2 = 10 / 2 = 5 cm. Area = πr² = π(5)² = 25π ≈ 78.5 cm².

A circle is inscribed in a square with a side length of 10 cm. What is the area of the circle?

A circle is inscribed in a square with a side length of 10 cm. What is the area of the circle?

Step 1: Identify the side length of the square, which is given as 10 cm.
Step 2: Calculate the radius of the inscribed circle by dividing the side length by 2. So, radius = 10 cm / 2 = 5 cm.
Step 3: Use the formula for the area of a circle, which is Area = πr².
Step 4: Substitute the radius into the area formula. So, Area = π(5 cm)².
Step 5: Calculate (5 cm)², which equals 25 cm².
Step 6: Multiply by π to find the area. So, Area = 25π cm².
Step 7: If needed, approximate the area using π ≈ 3.14. So, Area ≈ 25 * 3.14 = 78.5 cm².

Geometry – Understanding the relationship between a circle and a square, specifically how to derive the radius of the inscribed circle from the square's side length.
Area Calculation – Applying the formula for the area of a circle (A = πr²) to find the area based on the calculated radius.