mathematics
  Personalized »

KS3
 
 
 
Year 7
 
 
Year 8
 
 
Year 9

KS4
 
 
 
Year 10
 
 
Year 11

A-levels
 
 
 
Year 12 (AS)
 
 
Year 13 (A-levels)


physics
  Personalized »

 
 


KS4
 
 
 
KS4 Level Physics

A-levels
 
 
 
AS Level Physics
 
 
A-levels Physics


 
 
Private tutors
 
 
Find a tutor »


 


Unlock access to content
 
Select one option:



Free of charge
Unlock the chapter   "Area and Sector Area of a Circle"  



Unlock access to the solution of problems in this chapter.
Free of charge Price: 3.00 £

Continue »
Subscribe to OpenProf     If you do not get a better grade, you get your money back!
 


Unlock access to all problems solutions.
Available from 8.25 £ / month.
Continue »
mathematics UK Year 12 Mathematics (AS)
 
Solved problems for the chapter:
 

Area and Sector Area of a Circle

download pdf
View the theory »
Circle and arc for KS4
open
↓   Show theory [1]   ↓


Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:area_and_sector_area_of_a_circle/4700/


Example 1.

The area of the circle is 201.06 . Calculate the length of the arc and the area of the corresponding sector if the arc subtends an angle of 79° at the centre.

    
Example 2.

The length of the circular arc of a circle with area 78.54 is 9.08 cm. What angle does the arc subtend at the centre?

    
3.

An arc of length 3.09 cm lies on a circle with circumference 18.85 cm. Calculate the radius of the circle and the size of the corresponding center angle.

    
4.

The angle subtended at the centre of a circle with circumference 62.83 cm is 67°. Calculate the:


  • length of the arc and,

  • area of the corresponding sector formed by the angle.

    
5.

An arc of length 15.88 cm lies on a circle with a diameter of 14 cm. Calculate the:

  • size of the angle subtended at centre and,

  • circumference of the circle.

    
6.

A sector whose area is 0.66 is bounded by an arc of length 0.66 . Calculate the radius of the circle and the angle the sector subtended at the centre.

    
7.

An arc which subtends an angle 132° at the centre of a circle measures 16.13 cm. Calculate the area of the circle.

    
8.

The angle subtended by an arc of a circle with a diameter of 4 cm measures 22°. Calculate the:

  • length of the arc and,

  • the area of the circle.

    

9.

The area of a sector of a circle with a diameter of 2 is 0.98 . Calculate the value of the:

  • angle subtended at the centre and,

  • the circumference of the circle.

    
10.

A sector of a circle has an area 4.33 . If the sector subtends an angle of 31° at the centre of the circle, calculate the area of the circle.

    
11.

A sector of a circle of radius 6 cm subtends an angle of 77° at the centre. Calculate the:

  • area of the sector and,

  • circumference of the circle.

    
12.

The circumference of the outer and inner circles of the ring with the area 197.92 are in the ratio 8: 1. Calculate the radii of the circles of the ring .

    
13.

The radius of the outer circle of the ring with the area 84.82 measures 6 cm. Calculate the radius of the inner circle of the ring .

    
14.

The circumference of the inner circle of the ring with the area 103.67 measures 25.13 cm. Calculate the circumference of the outer circle of the ring .

    
15.

The area of a sector of a circle with radius 8 is 61.44 . Calculate the area of the corresponding segment.

    
16.

A segment of an area 20.99 subtends an angle 136° at the centre of the circle. Calculate the radius of the circle.

    
17.

An arc which subtends an angle of 42° measures 2.93. Calculate the area of the segment bonded by the arc.

    
18.

The central angle of an arc, , measures radians. Calculate its inscribed angle in degrees, minutes and seconds.

    

19.

In the square ABCD with a side of length , a circular arc with the center at the vertex B is drawn as shown in the figure:




Calculate the area and the perimeter of ​​the unshaded portion.

    
20.

A circle with radius is given:


  • Calculate the central angle belonging to a long chord . Draw a sketch.

  • % of the circle is colored red. What is the area of the colored part of the circle?

  • Calculate the perimeter and area of the square inscribed by the circle.

    
21.

The perpendicular projections on the hypotenuse of a right triangle divides it in the ratio . The hypotenuse measures . Construct the given triangle.

    
22.

The sum of an inscribed angle and its corresponding central angle is . What are the measures of the two angles? Express the answer to the nearest angular seconds.

    
23.

Determine the size of the angle .


    
24.

Points B, C and D lie on a circle with centre S. The tangents to the circle p and q intersect at point A. The angle measures . Draw the quadrilateral ABSD and determine its interior angles.


    
25.

A quadrilateral is drawn in a circle such that:




and




where r is the radius of the circle. Determine the interior angles of the quadrilateral.


    
26.

Triangle BDC is inscribed in a circle with centre S. Chord BC is the base of equilateral triangle ABC. The tangents to the circle p and q intersect at point A as shown in the figure below.


Determine the size of angle


   
27.

The equilateral triangle ABS has two vertices on the circle, and the third coincides with the centre of the circle as shown in the figure below. The angle measures . Determine .