Circles, arcs and sectors

The plate is circular, and its diameter is 27 cm.

Feb/March 2017

In the space provided, draw a circle with diameter 7 cm.

Feb/March 2018

The vertices of square $ABCD$ are positioned on the circle’s circumference, and the circle has radius 8 cm. The diagram presents square $ABCD$ drawn inside the circle. The shaded part is the segment lying above side $AD$.

Feb/March 2018

A car moves at a steady speed of 45 kilometres per hour for 5 minutes. The radius of each wheel on the car is 25 centimetres.

Feb/March 2020

A circle’s area is $25\pi\text{ cm}^2$.

Feb/March 2023

The diagram depicts a sector of a circle whose centre is O and whose radius measures 9 cm. The chord PQ has length 6 cm.

Feb/March 2023

The diagram depicts a circle with radius 12 cm, from which a sector has been cut out. The angle of the missing sector is $50^\circ$.

Feb/March 2024

The diagram depicts the larger segment of a circle with centre $O$ and radius $2.5\text{ m}$. This segment forms the cross-section of a tunnel whose height is $3\text{ m}$. The tunnel is $800\text{ m}$ long and its cross-section is constant along the whole length. The diagram is marked NOT TO SCALE.

Feb/March 2025

Calculate the radius of the circle.

May/June 2015

AB is an arc of a circle with centre $O$ and radius 9 cm. The length of arc $AB$ is $6\pi$ cm. The area of sector $AOB$ is $k\pi$ cm$^2$. The diagram shows sector $AOB$ with $OB = 9$ cm. The diagram is NOT TO SCALE.

May/June 2016

The sketch depicts a logo layout built from a sector together with two triangles. The sector, with centre $O$, has radius 8 cm and sector angle $210^{\circ}$. $AC = 8$ cm and $\angle ACB = 72^{\circ}$. The diagram is not drawn to scale.

May/June 2016

Calculate the area of a circle that has radius $5.1\text{ cm}$.

May/June 2018

Calculate how many sides the polygon has.

May/June 2018

The diagram depicts a semicircle whose diameter measures 9 cm. The diagram is not drawn to scale.

May/June 2019

The figure depicts a sector of a circle whose radius is $6.2\text{ cm}$ and whose sector angle is $217^{\circ}$. It is not drawn to scale.

May/June 2019

A circle has a radius of 42 cm.

May/June 2021

The diagram depicts a sector of a circle, with centre O and radius 9 cm. Its sector angle is $72^{\circ}$. The points are marked O, A and B. The drawing is not to scale.

May/June 2021

Calculate the perimeter of the shape.

May/June 2021

Draw a chord on the diagram.

May/June 2022

The figure depicts a square ABCD with side length k cm. MDE is a sector of a circle, centre D. E lies on the diagonal BD of the square. M is the midpoint of AD. NOT TO SCALE.

May/June 2022

The side length of a regular 12-sided polygon is 6 cm.

May/June 2022

The diagram illustrates shape $ABCD$, which is created from sectors of two circles with the same centre $O$. Each sector has an angle of $140^{\circ}$, $OC = 3.2\text{ cm}$ and $CB = 2.6\text{ cm}$. The area of the shape is $k\pi\text{ cm}^2$.

May/June 2023

The diagram illustrates a circle with a radius of 9 cm.

May/June 2024

The diagram depicts a figure formed from two semicircles that share a common centre. The radius of the larger semicircle is 7 cm, and the radius of the smaller semicircle is 4 cm.

May/June 2025

A diagram illustrates a sector of a circle with radius 3 cm and sector angle 60^{\circ}. It is not drawn to scale.

May/June 2025

The diagram depicts a sector of a circle with centre $O$. The arc length is $n\pi$ cm.

May/June 2025

The diagram depicts a sector of a circle with centre O. The circle has radius 6 cm, and the angle at the centre measures 40^{\circ}. Diagram not to scale.

May/June 2025

The figure represents a major sector of a circle with radius $7.5\text{ cm}$ and central angle $126^\circ$. It is not drawn to scale.

May/June 2025

The protractor has the form of a semicircle with radius $6.1\,\text{cm}$.

Oct/Nov 2015

A protractor has the shape of a semicircle with radius $6.1$ cm. The diagram is not drawn to scale.

Oct/Nov 2015

The diagram depicts a sector of a circle with radius $15\text{ cm}$ and angle $26\degree$, and it is not drawn to scale.

Oct/Nov 2015

$OAB$ is the sector of a circle with centre $O$, radius $8\text{ cm}$, and sector angle $30^\circ$. $BC$ is at right angles to $OA$. The diagram is labelled NOT TO SCALE.

Oct/Nov 2015

The pool is circular, and its radius is $8\text{ m}$.

Oct/Nov 2016

Write down the mathematical term for line PQ.

Oct/Nov 2016

The diagram illustrates a cross section of a cylinder with centre $O$ and radius $r$, resting on its side. Water in the cylinder reaches a depth of $18\text{ cm}$. The width, $AB$, across the water surface is $24\text{ cm}$.

Oct/Nov 2016

Calculate the area of a circle whose diameter is 9 cm.

Oct/Nov 2017

The diagram depicts a sector of a circle, with centre O and radius 6 cm. Its sector angle measures 30^{\circ}. The area of the shaded segment is $(k\pi - c)$ cm$^2$, with $k$ and $c$ being integers.

Oct/Nov 2017

The diagram depicts a sector of a circle, a triangle and a rectangle. The sector is centred at $O$, has radius $x$ cm and an angle of $270^\circ$. The rectangle measures $2x$ cm in length. The combined area of the shape is $kx^2$ cm$^2$.

Oct/Nov 2017

The figure depicts an equilateral triangle $ABC$ with each side measuring $10\text{ cm}$. $AMN$ is a sector of a circle, centred at $A$. $M$ is the midpoint of $AC$. The diagram is labelled NOT TO SCALE.

Oct/Nov 2018

A sector of a circle is drawn with radius $6\text{ cm}$ and central angle $72^\circ$. It is not drawn to scale. Its perimeter is $(p + q\pi)\text{ cm}$. A base is marked $6\text{ cm}$ and the angle at the centre is marked $72^\circ$.

Oct/Nov 2018

Calculate the area of a circle whose radius is 12 cm.

Oct/Nov 2019

Calculate the circumference of a circle whose radius is 4.5 cm.

Oct/Nov 2019

The figure has two sectors of circles that share the same centre. The angle is $45^{\circ}$. The inner radius is 3 cm and the outer radius is 5 cm. The shaded part lies between the two sectors. NOT TO SCALE.

Oct/Nov 2019

The circumference of a circle is $56\text{ mm}$.

Oct/Nov 2020

A circle sector is depicted with a central angle of $60^\circ$ and a radius measuring $7.5\text{ cm}$. The drawing is not drawn to scale.

Oct/Nov 2020

The figure shows $OAB$ as a sector of a circle with centre $O$. $OB = 8\,\text{cm}$ and the angle $AOB = 30^\circ$. $BP$ is drawn perpendicular to $OA$. The points are marked $O$, $A$, $B$, $P$. The diagram is NOT TO SCALE. The shaded part is $APB$.

Oct/Nov 2020

A circular disc has a circumference of 250 cm.

Oct/Nov 2021

The diagram illustrates a sector of a circle with radius 4.8 cm and a sector angle of $45^\circ$. The diagram is not drawn to scale.

Oct/Nov 2021

Calculate the radius of a circle whose circumference is 26 cm.

Oct/Nov 2021

The diagram depicts a sector of a circle, with centre $O$ and radius 12.6 cm. The central angle is $80^{\circ}$. The shaded part is a segment. The figure is marked NOT TO SCALE.

Oct/Nov 2021

Find the values of $x$, $y$ and $z$.

Oct/Nov 2021

A circular pond has a circumference of $130\text{ cm}$.

Oct/Nov 2022

A sector of a circle has radius $8\text{ cm}$ and perimeter $26\text{ cm}$. Calculate the angle of this sector.

Oct/Nov 2022

Calculate the upper bound for the triangle’s perimeter.

Oct/Nov 2022

A circle has a circumference of 59 cm.

Oct/Nov 2023

Calculate the area of a semicircle whose radius is 10 cm.

Oct/Nov 2023

The diagram illustrates a sector of a circle with radius $r$ cm and sector angle $72^\circ$. The arc length is 9.35 cm. Diagram is not drawn to scale.

Oct/Nov 2023

$ABCD$ forms a rhombus whose side length is $13.6\,$cm. The angle $ABC$ is $41^{\circ}$. $BAC$ is a sector of a circle centred at $B$, and $DAC$ is a sector of a circle centred at $D$.

Oct/Nov 2023

The diagram depicts a figure formed by the major sector $AOB$ together with triangles $OBC$ and $AOD$. Here $OB=6$ cm, $BC=2$ cm, the obtuse angle $AOC=135^\circ$ and angle $BCO=90^\circ$.

Oct/Nov 2023

A wheel's circumference measures 198.55 cm.

Oct/Nov 2024

Points $A$ and $B$ are located on a circle with centre $O$ and radius $r$. The diagram depicts triangle $AOB$ with a right angle at $O$. Since both $OA$ and $OB$ are radii of the circle, the circle has area $120\text{ cm}^2$.

Oct/Nov 2024

Points $A$, $B$, $C$ and $D$ are positioned on a circle. $ABCD$ makes a square with area $72\,\text{cm}^2$. The diagram below depicts the square within a circle. NOT TO SCALE.

Oct/Nov 2024

Find $w$.

Oct/Nov 2024

Calculate the area of the trapezium.

Oct/Nov 2024

The diagram depicts a semicircle. Its radius measures 8 cm.

Oct/Nov 2025

A circle has a diameter of 16 cm.

Oct/Nov 2025

The diagram depicts a sector of a circle with centre $O$ and radius $9\text{ cm}$. Its perimeter is $(18+2\pi)\text{ cm}$.

Oct/Nov 2025

The diagram depicts a major sector, AOB, of a circle. Its angle is 240^{\circ} and the radius measures 12 cm.

Oct/Nov 2025

The diagram represents a circle with centre O and radius 12 cm.

Oct/Nov 2025