Circle and Square Area Concepts

The video tutorial explains how to find the areas of a square and a circle, and then determine the area of the region inside the square but outside the circle. It begins by calculating the area of the square using the side length, which is equal to the circle's diameter. Next, it calculates the area of the circle using its radius, derived from the diameter. Finally, it finds the area of the yellow shaded region by subtracting the circle's area from the square's area, providing both exact and approximate values.

What is the diameter of the circle given in the problem?

• 8 miles

• 32 miles

• 4 miles

• 16 miles

How is the side length of the square related to the circle?

• It is twice the radius of the circle.

• It is equal to the diameter of the circle.

• It is equal to the radius of the circle.

• It is half the diameter of the circle.

What is the area of the square?

• 256 square miles

• 128 square miles

• 64 square miles

• 32 square miles

What is the formula for the area of a square?

• 2s

• s/2

• s²

• 4s

What is the radius of the circle?

• 2 miles

• 4 miles

• 8 miles

• 6 miles

Which formula is used to calculate the area of the circle?

• πr²

• πd

• 2πr

• πd²

What is the approximate area of the circle using π ≈ 3.14?

• 16 square miles

• 32 square miles

• 64 square miles

• 50.27 square miles

What is the exact area of the circle in terms of π?

• 20π square miles

• 8π square miles

• 12π square miles

• 16π square miles

How do you find the area of the yellow shaded region?

• Add the area of the square and the circle.

• Subtract the area of the circle from the area of the square.

• Multiply the area of the square by the area of the circle.

• Divide the area of the square by the area of the circle.

What is the approximate area of the yellow shaded region?

• 64 square miles

• 50.27 square miles

• 13.73 square miles

• 78 square miles