Mastering Arc Length and Sector Area in IB Maths

What is the formula for the arc length of a circle?

• L = 1/2 * r^2 * theta

• L = r * theta

• L = 2 * pi * r

• L = pi * r^2

What does the arc length formula L = r * theta imply about the relationship between r and theta?

• They are inversely proportional

• Theta is squared in the relationship

• They are directly proportional

• They are unrelated

What does the arc length formula simplify to when the angle theta is 2π radians?

• The area of the circle

• The radius of the circle

• The diameter of the circle

• The circumference of the circle

What is the formula for the area of a sector of a circle?

• A = r * theta

• A = 2 * pi * r

• A = pi * r^2

• A = 1/2 * r^2 * theta

How does the sector area formula simplify when theta is 2π radians?

• It becomes the area of the circle

• It becomes the diameter of the circle

• It becomes the circumference of the circle

• It remains unchanged

In a practical example, if a circle has a radius of 10 meters and the angle is 4 radians, what is the arc length?

• 10 meters

• 14 meters

• 20 meters

• 40 meters

Using the same example, what would be the sector area?

• 50 square meters

• 100 square meters

• 400 square meters

• 200 square meters

What practical use does the sector area formula have in everyday applications?

• Estimating travel distances

• Calculating areas of fields

• Designing circular objects

• All of the above

How is the concept of arc length applied in satellite imaging?

• To determine the minimum angle for image resolution

• To calculate the distance between satellites

• To measure the size of the earth

• To calculate the speed of the satellite

What is the Rayleigh criterion used for in physics?

• To determine the minimum resolvable angle

• To study thermal dynamics

• To measure the intensity of light

• To calculate force