Understanding Annulus Area Concepts

The video tutorial introduces the concept of an annulus, a circular shape with a hole in the middle, and explains how to calculate its area using the formula: π(R² - r²). The tutorial provides three examples with different shaded regions (red, blue, and green) to demonstrate the application of the formula. Each example involves identifying the radii of the large and small circles, substituting them into the formula, and calculating the shaded area using a calculator.

What is an annulus?

• A solid circle

• A circle with a hole in the middle

• A triangle with a hole

• A square with a hole

Which of the following best describes the shape of an annulus?

• A square with a smaller square removed

• A triangle with a smaller triangle removed

• A circle with a smaller circle removed

• A rectangle with a hole

What is the formula to find the area of an annulus?

• π × (R + r)^2

• π × (R^2 - r^2)

• π × (R^2 + r^2)

• π × (R - r)^2

In the formula for the area of an annulus, what does 'R' represent?

• The radius of the smaller circle

• The radius of the larger circle

• The diameter of the smaller circle

• The diameter of the larger circle

In the first example, what is the radius of the larger circle?

• 11 cm

• 3 cm

• 8 cm

• 5 cm

In the first example, what is the radius of the smaller circle?

• 3 cm

• 11 cm

• 8 cm

• 5 cm

What is the area of the red shaded region in the first example?

• 100.00 square cm

• 351.86 square cm

• 122.52 square cm

• 141.57 square cm

In the second example, what is the radius of the larger circle?

• 5 cm

• 8 cm

• 11 cm

• 3 cm

In the second example, what is the radius of the smaller circle?

• 5 cm

• 8 cm

• 11 cm

• 3 cm

What is the area of the blue shaded region in the second example?

• 141.57 square cm

• 100.00 square cm

• 122.52 square cm

• 351.86 square cm