Arc length of a sector
Difficulty: ★☆☆
In the diagram, \(ABC\) is a sector of a circle with centre \(A\) and radius \(8\text{ m}\). The size of angle \(BAC\) is \(0.65\text{ rad}\).
Find the length of arc \(BC\).
Give your answer to 2 significant figures.
Area of a shaded region in a sector
Difficulty: ★★☆In the diagram, \(ABC\) is a sector of a circle with centre \(A\) and radius \(8\text{ m}\). The size of angle \(BAC\) is \(0.65\text{ rad}\), and \(D\) is the midpoint of \(AC\).
Find the area of the shaded region \(BCD\).
Give your answer to 3 significant figures.
Chords, minor segments and major segments: check 1
Difficulty: ★★☆Maths4U Original · Short practice
For radius \(r\) and minor angle \(0<\theta<\pi\) in radians, which is the minor segment area?Choose one answer.
Chords, minor segments and major segments: check 2
Difficulty: ★★☆Maths4U Original · Short practice
A radius-4 cm circle has a minor sector angle \(\pi/2\). The minor segment area is \((4\pi-k)\) square cm. Find \(k\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Chords, minor segments and major segments: check 3
Difficulty: ★★☆Maths4U Original · Short practice
A chord subtends \(\pi/3\) at the centre of a radius-9 cm circle. Find the chord length in cm.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Chords, minor segments and major segments: check 4
Difficulty: ★★☆Maths4U Original · Short practice
The minor segment has area \(S\) in a circle of radius \(r\). What is the major segment area?Choose one answer.
Annular sectors and composite boundaries: check 1
Difficulty: ★★☆Maths4U Original · Short practice
An annular sector has outer radius 7 cm, inner radius 3 cm, angle 0.8 radians. Find its area in square cm.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Annular sectors and composite boundaries: check 2
Difficulty: ★★☆Maths4U Original · Short practice
An annular sector has radii 7 cm and 3 cm, angle 0.8 radians. Find its complete perimeter in cm.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Annular sectors and composite boundaries: check 3
Difficulty: ★★☆Maths4U Original · Short practice
Two non-overlapping sectors of the same circle have angles 0.6 and 0.9 radians. If the radius is 4 cm, find their total area in square cm.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Annular sectors and composite boundaries: check 4
Difficulty: ★★☆Maths4U Original · Short practice
Two equal sectors overlap in a region of area \(B\). Each sector has area \(A\). What is their union area?Choose one answer.
Chords, minor segments and major segments: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
A minor sector has area 23 square cm. The triangle formed by its two radii and chord has area 9 square cm. Find the minor segment area in square cm.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Chords, minor segments and major segments: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
A radius-6 cm sector has angle \(\pi/2\). Its minor segment area is \((9\pi-k)\) square cm. Find k.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Chords, minor segments and major segments: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
A radius-11 cm circle has a chord subtending \(\pi/3\). Find the chord length in cm.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Chords, minor segments and major segments: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
In a radius-12 cm circle, the minor segment area is \(9\pi\) square cm. The major segment area is \(k\pi\) square cm. Find k.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Annular sectors and composite boundaries: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
An annular sector has radii 8 cm, 2 cm and angle 0.6 radians. Find its area in square cm.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Annular sectors and composite boundaries: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
For annular-sector radii 8 cm, 2 cm and angle 0.6 radians, find the full perimeter in cm.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Annular sectors and composite boundaries: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
Two non-overlapping radius-5 cm sectors have angles 0.7 and 0.9 radians. Find the total area in square cm.Enter one number or fraction. Round decimals to at least six decimal places when needed.
Annular sectors and composite boundaries: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
Two sectors each have area 18 square cm. Their overlap is 5 square cm. Find the union area in square cm.Enter one number or fraction. Round decimals to at least six decimal places when needed.