MENSURATION II

Length of an Arc, Area of Sector, Length of a chord, Perimeter

 

Question1

 

 

 

 

 

 

Find the area of the shaded segment in the figure above (UME 1980, Question 50)

 

Solution

 

Question 2

A sector of a circle is bounded by two radii 7cm long and arc of length 6cm. Find the area of the sector  (UME 1982 Question 18)

 

Solution

 

 

 

 

 

 

Question 3

Two distinct sectors in the same circle subtend 100^o and 30^o respectively at the center of the circle. Then the corresponding lengths of arcs are in the ratio (UME 1980, Question 47)

 

Solution

The radius of the two arcs will be equal, since they are of the same circle. The ratio of the their length will be 100: 30 = 10:3

 

Question 4

PQR is the diameter of a semicircle RSP with center at Q and radius of length 3.5cm. If , find the perimeter of the figure PTRS ,  (UME 1983, Question 45)

 

 

Solution

 

 

 

 

 

 

 

                              

 

 

 

 

 

 

 

 

 

Question 5

 

 

 

 

 

 

 

In the figure above, the area of the shaded segment is (UME 1985, Question 47) 

 

Solution

Question 6

An arc of circle of radius 6cm is 8cm long. Find the area of the sector

 

Solution

Question 7

Calculate the length of an arc of circle of diameter 8cm which subtends an angle of 22^o at the center  (UME 1993, Question 27)

 

Solution

 

Question 8

Find the area of the sector of the circle with radius 3cm. If the angle of the sector is 60^o (UME 1993, Question 37)

 

 

Question 9

Calculate the perimeter in cm of a sector of a circle of radius 8cm and angle 45^o

 

Solution

Question 10

A chord of a circle of diameter 42cm subtends an angle of 60^o at the center of the circle. Find the length of the minor arc. (UME 1997,Question 28)

 

Solution

 

Question 11

A chord of a circle radius √3 cm subtends an angle of 60^o on the circumference of the circle. Find the length of the chord

 

Solution

 

 

 

 

 

 

 

 

 

 

                                         

 

                QUESTION 12

A  chord is drawn 5cm away from the centre of a circle of radius 13cm. Calculate the length of the chord. (UME 2009 Question 28 Set A U03)

A) 7cm   B)9cm    C) 12cm   D)  24 cm

Solution

 

 

 

 

 

 

 

 

 

          

The length of the chord is 24cm

            Answer: Option D