IB Mathematics Applications & Interpretation Question Type 2: Calculating the Arc Length Given a Radius and Specific Angle Exercises

A car travels $200$ m along a circular track of radius $50$ m. Find the central angle in degrees that it subtends.

If an arc length equals twice the radius in a circle of radius $3\text{ m}$, find the subtended angle in radians.

A pendulum of length $L$ swings through $0.3$ radians and describes an arc of $0.15$ m. Find $L$.

An arc on a circle of radius $7$ cm has length $5\pi$ cm. Determine the central angle in radians.

A sector of a circle has radius $8\text{ cm}$ and arc length $6\pi \text{ cm}$. Find the central angle in radians.

Find the ratio of arc lengths subtended by angles $\frac{\pi }{6}$ and $\frac{\pi }{3}$ on the same circle of radius $7$ cm.

Find the arc length of a circle with radius $10$ cm and central angle $2$ radians.

A wheel of radius $0.75$ m completes $3$ full revolutions. Find the total distance travelled by a point on its rim.

On a circle of radius $9\text{ m}$, find the difference between the arc lengths subtended by angles $\frac{\pi }{3}$ and $\frac{\pi }{6}$ radians.

Two concentric circles have radii $6\text{ cm}$ and $10\text{ cm}$. Calculate the difference in their arc lengths for a common central angle of $\frac{\pi }{4}$ radians.

Calculate the arc length of a circle with radius $4$ m subtended by a central angle of $\frac{\pi }{5}$ radians.

An object moves along a circle of radius $5$ m from angle $0.2$ rad to $1.4$ rad. Calculate the distance it travels along the arc.

Determine the radius of a circle if an arc of length $12$ m subtends an angle of $0.6$ radians.

A circle has radius $3\text{ m}$. Find the length of the arc subtended by a $90^{\circ }$ angle.

The radius of a circle increases from $5$ cm to $9$ cm while the central angle remains $2$ radians. Find the increase in arc length.

Calculate the length of a semicircular arc on a circle of radius $5$ m.

A circle has radius $12\text{ cm}$. Calculate the length of the arc subtended by a $72^{\circ }$ angle.