Question

solve plz
u will take 30 points of it

Answer 1

Answer:

Step-by-step explanation:

8. Figure depicts a racing track whose left and right ends are semicircular.

The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find:

(i) the distance around the track along its inner edge.

(ii) the area of the track.

Ans. (i)Distance around the track along its inner edge

=  

=  =  =  m

(ii)Area of track =  

=  

=  =

Answer 2

Solution:

(i)

Radius of inner semi-circle =602=30 m

Circumference of inner semicircle =π.r=227×30=6607 m

The distance around the track along its inner edge=length of two inner parallel lines each equal to 106 m + circumference of two inner semicircles.

=106+106+6607+6607=28047 m

(ii)

Area of the track = area of two rectangles formed in the track + area enclosed by the semi-circles (1)

Area of rectangle = length x breadth = 106 x width of track = 106 x 10=1060 m

⇒ Area of two rectangles=2 x 1060=2120 m (2)

Diameter of bigger semi-circle=60+width of track + width of track=60+10+10=80 m

⇒ Radius of bigger semi-circle =802=40 m

Area enclosed by left semi-circles=Area of bigger semi-circle-area of smaller semi-circle =π.2(r1)2−π.(r2)2

=π2.(r12−r22)=π2.(402−302)=2214(1600−900)=1100 m2

⇒ Area enclosed by left and right semi-circles=2 x 1100=2200 m2 (3)

Putting (2) and (3) in (1), we get

Area of the track = area of two rectangles formed in the track + area enclosed by the semi-circles

=2120+2200=4320 m2