GCSE Secondary Maths Age 13-17 - Geometry & Measures: Area of a Circle - Problem - Explained

The video tutorial explains how to solve a geometry problem involving a square inscribed in a circle. The task is to find the side length of the square, given the area of the circle. The instructor highlights the importance of understanding the geometric relationship between the square and the circle, particularly how the diagonal of the square is the diameter of the circle. The solution involves calculating the diameter using the circle's area and applying Pythagoras' theorem to find the side length. The tutorial emphasizes the importance of planning and understanding the problem to achieve the correct solution.

What is the area of the circle in which the square is inscribed?

• 81 cm²

• 64 cm²

• 49 cm²

• 36 cm²

What is the relationship between the diagonal of the square and the circle?

• The diagonal is equal to half the diameter of the circle.

• The diagonal is equal to the diameter of the circle.

• The diagonal is equal to the circumference of the circle.

• The diagonal is equal to the radius of the circle.

How do you calculate the radius of the circle from its area?

• Divide the area by 2π and take the square root.

• Multiply the area by 2π and take the square root.

• Multiply the area by π and take the square root.

• Divide the area by π and take the square root.

What is the formula used to find the side length of the square using Pythagoras' theorem?

• a² + b² = 2c²

• a² - b² = 2c²

• a² - b² = c²

• a² + b² = c²

What is the calculated diameter of the circle?

• 8.94 cm

• 7.89 cm

• 6.28 cm

• 9.78 cm

What is the final calculated side length of the square, rounded to three significant figures?

• 5.61 cm

• 5.59 cm

• 5.58 cm

• 5.60 cm

How many marks were awarded for finding the radius in the problem?

• Two marks

• Four marks

• Three marks

• One mark