A circular lawn is surrounded by a jogging track 7m wide. If the circumference of the lawn is 88m, find: (i) Area of jogging track. (ii) Circumference of the track.
Answers
GIVEN :-
- A circular lawn is surrounded by a jogging track 7 m wide.
- Circumference of Lawn is 88 m.
TO FIND :-
- Area of jogging track.
- circumference of the jogging track.
SOLUTION :-
Let the radius of circular lawn be "r" and the radius of jogging track be "R".
✭ Radius of circular lawn,
As we know that the circumference of a circle is given by,
➟ Circumference = 2πr.
➟ 88 = 2πr
➟ 88 = 2 × 22/7 × r
➟ 88 = 44/7 × r
➟ r = (88 × 7)/44
➟ r = 2 × 7
➟ r = 14 m.
✭ Area of circular lawn,
As we know that the area of circle is given by,
➙ Area = πr²
➙ Area = 22/7 × 14 × 14
➙ Area = 22 × 2 × 14
➙ Area = 616 m².
✯ Radius of jogging track,
➙ R = r + width.
➙ R = 14 + 7
➙ R = 21 m.
✷ Area of outer circle,
As we know that the area of circle is given by,
➟ Area = πr².
➟ Area = 22/7 × 21 × 21
➟ Area = 22 × 3 × 21
➟ Area = 1386 m².
✭ Area of jogging track,
⇻ Area of track = Area(outer circle) - Area(Lawn)
⇻ Area of track = 1386 m² - 616 m²
⇻ Area of track = 770 m².
✭ Circumference of jogging track,
As we know that the circumference of a circle is given by,
⇻ Circumference = 2πR.
⇻ Circumference = 2 × 22/7 × 21
⇻ Circumference = 44/7 × 21
⇻ Circumference = 44 × 3
⇻ Circumference = 132 m.
