A circle is inscribed in a square of side 10 cm. What is the area of the circle?
Practice Questions
Q1
A circle is inscribed in a square of side 10 cm. What is the area of the circle? (2019)
78.5 cm²
100 cm²
50 cm²
25 cm²
Questions & Step-by-Step Solutions
A circle is inscribed in a square of side 10 cm. What is the area of the circle? (2019)
Step 1: Identify the side length of the square, which is given as 10 cm.
Step 2: Understand that the circle is inscribed in the square, meaning the circle touches all four sides of the square.
Step 3: Calculate the radius of the circle. Since the diameter of the circle is equal to the side length of the square, the radius is half of the side length: 10 cm / 2 = 5 cm.
Step 4: Use the formula for the area of a circle, which is Area = π * r².
Step 5: Substitute the radius into the area formula: Area = π * (5 cm)².
Step 6: Calculate (5 cm)², which is 25 cm².
Step 7: Multiply by π to find the area: Area = π * 25 cm².
Step 8: Use the approximate value of π (3.14) to calculate the area: Area ≈ 3.14 * 25 cm² = 78.5 cm².
Circle Area Calculation – Understanding how to calculate the area of a circle using the formula A = πr², where r is the radius.
Relationship Between Circle and Square – Recognizing that the diameter of the inscribed circle is equal to the side length of the square.
