IB Maths AI SL 3.4 Arc Length and Sector Area Questions

Practise converting angles and using arc-length or sector-area formulae to find unknown dimensions, checking units, diagrams and rounding.

Exam points

Convert between degrees and circle fractions as needed to calculate arc length or sector area using the given angle.
Apply arc-length and sector-area formulae to determine an unknown radius, angle, length or area.
Interpret the result in a diagram or applied context with correct units and rounding.

Learn this topic

Study SL 3.4—Arc length and sector area conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 5]

The Scheveningen Ferris wheel's lowest point is 8 m above sea level, and its highest point is 45 m above sea level.

Figure for Question IB Maths AI SL 3.4 Arc Length and Sector Area Questions question 1 — IB Maths AI SL

(a)

Show that the radius of the Ferris wheel is 18.5 m .

[ 1 ]

$\frac{45-8}{2} \quad A1$ $18.5(\mathrm{~m})$ AG
Note: Use of 18.5 in the calculation is reverse engineering, and falls short of the demand of the command term "Show that'. In such cases, award A0.

(b)

Calculate the circumference of the Ferris wheel.

There are pods, equally spaced around the wheel, that carry passengers.

[ 1 ]

$\quad(2 \pi \times 18.5=) 116(116.2389 \ldots, 37 \pi)(\mathrm{m})$ .

(c)

When the wheel rotates $10^{\circ}$ , find the distance that a pod travels along the circumference.

The height in metres, above sea level, of a particular pod is modelled by the function:

h(t)=a \sin (b t)+d, \text { for } a, b>0

where t is the time, measured in minutes.
The wheel takes 15 minutes to complete 1 revolution.

[ 3 ]

recognition the distance is the arc length

\begin{aligned} & \frac{10^{\circ}}{360^{\circ}} \times 2 \pi \times 18.5 \text { OR } \frac{116.2389 \ldots}{36} \\ & =3.23\left(3.228859 \ldots, \frac{37 \pi}{36}\right)(\mathrm{m}) \end{aligned}

All question bank results loaded

Learn this topic

IB Maths AI SL 3.4 Arc Length and Sector Area Questions question 1

Question (a)

Question (b)

Question (c)