# A square lawn of side 100m has a circular flower bed in the centre. If area of lawn, excluding flower bed is 8614 m^2...

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A square lawn with side 100 m long has a circular flower bed in the centre. If the area of the lawn, excluding the flower bed is 8614 m^2, the radius of the circular flower bed is

posted Oct 14, 2015

+1 vote

area of square lawn = 100*100= 10000 m^2
area of the flower bed = area of lawn - area excluding flower bed = 10000-8614=1386 m^2
now,
πr^2= 1386
r^2= 441
r= √441 =21
so, radius of the flower bed = 21m

Area of square lawn=A
=side^2
=100^2
=10000 M^2

Area of circle =C=pi/4*dia.^2..... (i)

Area of remaining square =B=8614M^2

Since
A=B+C
i. e.
C=A-B
C=10000-8614
C=1386M^2.... (ii)

By equating (i) & (ii)
Pi/4*dia.^2=1386

Evaluate from above
dia. =42m

So radius of flower bed is 21 m

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