In given 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

Question

In given 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

Filo · Accepted Answer

The distance around the track along its inner edge

= EF + H G

+

circumference of semicircle with diameter

E H +

circumference of semicircle with diameter

FG

circumference of semicircle with diameter

E H

+

Circumference of semicircle with diameter

FG

= 2 \times π \times 30 = 60 π m

∴

The distance around the track along its inner edge

= 60 π + 106 + 106

= \frac{2804}{7} m

∴

Area of track

=

Area of rectangle

A BFE

+

Area of rectangle

H GC D

+

(Area of semicircle with diameter

A D

-

Area of semicircle with diameter

E H

)

+

(Area of semicircle with diameter

BC

-

Area of semicircle with diameter

FG

)

= (106 \times 10)

+

(106 \times 10)

+

(\frac{π}{2} \times 40 \times 40 - \frac{π}{2} \times 30 \times 30)

+

(\frac{π}{2} \times 40 \times 40 - \frac{π}{2} \times 30 \times 30)

= 2120 + 2200 = 4320 m^{2}

Question Text	In given 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
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified