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mathematics UK Year 12 Mathematics (AS)
 
Solved problems for the chapter:
 

Length of an arc

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Circle and arc for KS4
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:length_of_an_arc/5405/


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 132° at the centre.

    
Example 2.

The length of the circular arc of a circle with area 78.54 is 7.07 cm. What angle does the arc subtend at the centre?

    
3.

An arc of length 2.79 cm lies on a circle with circumference 50.27 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 6.28 cm is 166°. Calculate the:


  • length of the arc and,

  • area of the corresponding sector formed by the angle.

    
5.

What angle do the hour and minute hands enclose when the time is ?

    
6.

An arc of length 2.86 cm lies on a circle with a diameter of 2 cm. Calculate the:

  • size of the angle subtended at centre and,

  • circumference of the circle.

    
7.

A sector with a central angle, , has an area of . Draw a sketch and calculate the length of the arc that that formed the sector.

    
8.

An arc which subtends an angle 106° at the centre of a circle measures 16.65 cm. Calculate the area of the circle.

    

9.

The angle subtended by an arc of a circle with a diameter of 6 cm measures 36°. Calculate the:

  • length of the arc and,

  • the area of the circle.

    
10.

An arc which subtends an angle of 49° measures 6.84. Calculate the area of the segment bonded by the arc.

    
11.

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.