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SL 3.4—The circle, arc and area of sector, degrees only - IB Questionbank | RevisionDojo

Practice SL 3.4—The circle, arc and area of sector, degrees only with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SLPaper 2

A circular garden has a radius of 7 m. A path runs along a quarter of the perimeter.

Find the length of the path.

[3]

Question 2

SLPaper 2

The arc length of a sector is $20\text{ cm}$ and the radius is $r$ .

If the central angle is $100^{\circ}$ , find $r$ .

[5]

Question 3

SLPaper 2

A circular track has radius $25 \text{ m}$ . A runner jogs along a path that covers an angle of $135^{\circ}$ .

Calculate the distance the runner travels.

[4]

Question 4

SLPaper 1

Joey is making a party hat in the form of a cone. The hat is made from a sector, $AOB$ , of a circular piece of paper with a radius of $18\text{ cm}$ and $\text{AOB} = \theta$ as shown in the diagram.

To make the hat, sides $[OA]$ and $[OB]$ are joined together. The hat has a base radius of $6.5\text{ cm}$ .

Write down the perimeter of the base of the hat in terms of $\pi$ .

[1]

Find the value of $\theta$ .

[2]

Find the surface area of the outside of the hat.

[2]

Question 5

SLPaper 2

A circular sign has a shaded sector with angle $45^{\circ}$ .

If the radius is $4\text{ m}$ , find the length of the arc.

[3]

Question 6

SLPaper 1

In a circular playground with a diameter of $10\text{ cm}$ , a rope is stretched across the playground, forming a chord of length $8\text{ cm}$ .

Find the distance from the centre of the circle to the midpoint of the chord.

[2]

Calculate the angle subtended by the chord at the centre of the circle, giving your answer in degrees.

[2]

Determine the area of the minor segment of the circle bounded by the chord and the arc.

[4]

Question 7

HLPaper 1

A circle has a radius of 5 cm.

Express an angle of $240^\circ$ in radians.

[2]

Find the area of the sector subtended by the angle $240^\circ$ .

[4]

Determine the length of the arc subtended by the angle $240^\circ$ .

[3]

Question 8

SLPaper 2

The arc length of a sector is 18.85 cm and the angle is $108^{\circ}$ .

Find the radius of the circle.

[5]

Question 9

SLPaper 2

A rotating wheel has a radius of $0.5\text{ m}$ . A mark on the rim travels along an arc of $1.75\text{ m}$ .

Find the angle the wheel has rotated through in degrees, and the number of rotations this represents.

[6]

Question 10

SLPaper 2

In a triangular plot of land $\triangle ABC$ , the sides $AB$ and $BC$ measure $5$ m and $7$ m, respectively, with an angle $\angle ABC = 60^\circ$ between them.

Use the cosine rule to calculate the length of side $AC$ , which represents the boundary distance across the plot.

[5]

Calculate the area of the triangle using the formula $\frac{1}{2} ac \sin B$ to determine the total land area available for use.

[3]

Using your answer from Part 1, determine whether the triangle is acute, right-angled, or obtuse. Justify your answer.

[3]

Paper

Level

Question 1

SLPaper 2

A circular garden has a radius of 7 m. A path runs along a quarter of the perimeter.

Find the length of the path.

[3]

Question 2

SLPaper 2

The arc length of a sector is $20\text{ cm}$ and the radius is $r$ .

If the central angle is $100^{\circ}$ , find $r$ .

[5]

Question 3

SLPaper 2

A circular track has radius $25 \text{ m}$ . A runner jogs along a path that covers an angle of $135^{\circ}$ .

Calculate the distance the runner travels.

[4]

Question 4

SLPaper 1

To make the hat, sides $[OA]$ and $[OB]$ are joined together. The hat has a base radius of $6.5\text{ cm}$ .

Write down the perimeter of the base of the hat in terms of $\pi$ .

[1]

Find the value of $\theta$ .

[2]

Find the surface area of the outside of the hat.

[2]

Question 5

SLPaper 2

A circular sign has a shaded sector with angle $45^{\circ}$ .

If the radius is $4\text{ m}$ , find the length of the arc.

[3]

Question 6

SLPaper 1

In a circular playground with a diameter of $10\text{ cm}$ , a rope is stretched across the playground, forming a chord of length $8\text{ cm}$ .

Find the distance from the centre of the circle to the midpoint of the chord.

[2]

Calculate the angle subtended by the chord at the centre of the circle, giving your answer in degrees.

[2]

Determine the area of the minor segment of the circle bounded by the chord and the arc.

[4]

Question 7

HLPaper 1

A circle has a radius of 5 cm.

Express an angle of $240^\circ$ in radians.

[2]

Find the area of the sector subtended by the angle $240^\circ$ .

[4]

Determine the length of the arc subtended by the angle $240^\circ$ .

[3]

Question 8

SLPaper 2

The arc length of a sector is 18.85 cm and the angle is $108^{\circ}$ .

Find the radius of the circle.

[5]

Question 9

SLPaper 2

A rotating wheel has a radius of $0.5\text{ m}$ . A mark on the rim travels along an arc of $1.75\text{ m}$ .

Find the angle the wheel has rotated through in degrees, and the number of rotations this represents.

[6]

Question 10

SLPaper 2

In a triangular plot of land $\triangle ABC$ , the sides $AB$ and $BC$ measure $5$ m and $7$ m, respectively, with an angle $\angle ABC = 60^\circ$ between them.

Use the cosine rule to calculate the length of side $AC$ , which represents the boundary distance across the plot.

[5]

Calculate the area of the triangle using the formula $\frac{1}{2} ac \sin B$ to determine the total land area available for use.

[3]

Using your answer from Part 1, determine whether the triangle is acute, right-angled, or obtuse. Justify your answer.

[3]

Paper

Level

Question 1

SLPaper 2

A circular garden has a radius of 7 m. A path runs along a quarter of the perimeter.

Find the length of the path.

[3]

Question 2

SLPaper 2

The arc length of a sector is $20\text{ cm}$ and the radius is $r$ .

If the central angle is $100^{\circ}$ , find $r$ .

[5]

Question 3

SLPaper 2

A circular track has radius $25 \text{ m}$ . A runner jogs along a path that covers an angle of $135^{\circ}$ .

Calculate the distance the runner travels.

[4]

Question 4

SLPaper 1

To make the hat, sides $[OA]$ and $[OB]$ are joined together. The hat has a base radius of $6.5\text{ cm}$ .

Write down the perimeter of the base of the hat in terms of $\pi$ .

[1]

Find the value of $\theta$ .

[2]

Find the surface area of the outside of the hat.

[2]

Question 5

SLPaper 2

A circular sign has a shaded sector with angle $45^{\circ}$ .

If the radius is $4\text{ m}$ , find the length of the arc.

[3]

Question 6

SLPaper 1

In a circular playground with a diameter of $10\text{ cm}$ , a rope is stretched across the playground, forming a chord of length $8\text{ cm}$ .

Find the distance from the centre of the circle to the midpoint of the chord.

[2]

Calculate the angle subtended by the chord at the centre of the circle, giving your answer in degrees.

[2]

Determine the area of the minor segment of the circle bounded by the chord and the arc.

[4]

Question 7

HLPaper 1

A circle has a radius of 5 cm.

Express an angle of $240^\circ$ in radians.

[2]

Find the area of the sector subtended by the angle $240^\circ$ .

[4]

Determine the length of the arc subtended by the angle $240^\circ$ .

[3]

Question 8

SLPaper 2

The arc length of a sector is 18.85 cm and the angle is $108^{\circ}$ .

Find the radius of the circle.

[5]

Question 9

SLPaper 2

A rotating wheel has a radius of $0.5\text{ m}$ . A mark on the rim travels along an arc of $1.75\text{ m}$ .

Find the angle the wheel has rotated through in degrees, and the number of rotations this represents.

[6]

Question 10

SLPaper 2

In a triangular plot of land $\triangle ABC$ , the sides $AB$ and $BC$ measure $5$ m and $7$ m, respectively, with an angle $\angle ABC = 60^\circ$ between them.

Use the cosine rule to calculate the length of side $AC$ , which represents the boundary distance across the plot.

[5]

Calculate the area of the triangle using the formula $\frac{1}{2} ac \sin B$ to determine the total land area available for use.

[3]

Using your answer from Part 1, determine whether the triangle is acute, right-angled, or obtuse. Justify your answer.

[3]

SL 3.4—The circle, arc and area of sector, degrees only Questionbank