A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, find the area of the road
NCERT Class X
Mathematics - Exemplar Problems
Chapter _AREA RELATED TO CIRCLES
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167
Hi,
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.
*****
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.
*****
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52
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