A circle is inscribed in a square. If the side of the square is 8 cm, what is th

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Question: A circle is inscribed in a square. If the side of the square is 8 cm, what is the area of the circle?

Options:

Correct Answer: 50.24 cm²

Solution:

Radius of the circle = side/2 = 8/2 = 4 cm. Area = πr² = π(4)² = 16π ≈ 50.24 cm².

A circle is inscribed in a square. If the side of the square is 8 cm, what is the area of the circle?

A circle is inscribed in a square. If the side of the square is 8 cm, what is the area of the circle?

Step 1: Identify the side length of the square, which is given as 8 cm.
Step 2: Calculate the radius of the inscribed circle. The radius is half of the side length of the square. So, radius = side / 2 = 8 cm / 2 = 4 cm.
Step 3: Use the formula for the area of a circle, which is Area = πr², where r is the radius.
Step 4: Substitute the radius into the area formula. Area = π(4 cm)².
Step 5: Calculate (4 cm)², which is 16 cm².
Step 6: Multiply by π to find the area. Area = 16π cm².
Step 7: If needed, approximate the area using π ≈ 3.14. So, Area ≈ 16 * 3.14 = 50.24 cm².

Geometry – Understanding the relationship between a square and an inscribed circle, including how to calculate the radius and area.
Area Calculation – Applying the formula for the area of a circle (A = πr²) using the radius derived from the square's dimensions.