a circular Park surrounded by a 21 m wide if the radius of the park is 105 M find the area of the road
Answers
Let radius of the circular park = r = 105 m
Width of the road surrounded by the
Park = w = 21 m
Radius of the outer circle = R = r + w
R = 105 + 21 = 126 m
Area of the road = area of the outer
circle - area of the inner circle
A = pi × R ^2 - pi × r ^2
A = pi ( R ^2 - r ^2 )
A = pi × ( R + r ) ( R - r )
A = pi × ( R + r ) × w
Substitute the values
A = 22/ 7 × ( 126 + 105 ) × 21
A = 22 × 231 × 3
A = 15246 square meters.
Therefore,
Area of the road = 15246sq meters
I hope this will useful to you.
Radius of park (r) = 105 m
Width of road = 21 m
Radius of outer road (R) = 105 + 21 = 126 m
Area of Road =
Area of Road = Area of Bigger Circle - Area of Smaller Circle.
The radius of bigger circle, R = radius of park + width of road = 105 + 21 = 126 m
Radius of smaller circle, r = radius of park = 105m
Now,
Aread of road = (pi)R2 - (pi)r2 = (pi) * [1262 - 1052]
= 22/7 * [ (32 * 7 * 2)2 - (5 * 3 * 7)2] ---- here 3 and 7 are common take them out-- = 22/7 * 72*32 * [(3*2)2 - (5)2] --- simplify the squares in bracket and cancel the 72 with 7 you will get something like this:-
= 22*7*9 [36-25] = 22*63[11] = 15246 m2