Question

A road 3.5m wide surrounds a circular plot whose circumference is 44m. find the cost of paving the road at 20 Rs per m square.(take π=22/7)

Answer 1

Circumference of the circular plot = 44m
$2\pi \: r = 44 \: cm$
$r = 22 \times \frac{7}{22} = 7cm$
radius of the whole figue along with the road =
$7 + 3.5 = 10.5cm$
area of the road =
$\pi( {10.5}^{2} - {7}^{2} )$
$= 192.5 {cm}^{2}$
cost of paving = 192.5* 20 = ₹3850

Answer 2

The circumference of plot = 44
2 * 22/7*r =44
r = 44*7/2**22
r =7m
area of plot = 22/7 * 7*7
= 154 m ^2
as the road surrounds the plot therefore ,

radius of circle + widness of road = the radius of road from plot...
radius of road from plot = 7 + 3.5
= 10.5 m

Area of road with plot = 22/7*10.5*10.5
= 22/7 *105/10*105/10
= 11*3*21/2
= 346.5 m ^2
Area of road = area of road with plot - area of plot.
= 346.5 - 154
= 192.5m^2

Cost of paving road 1 m = Rs 20
"""""""""""""""""""""" 192.5 m = 20* 192.5
= 3950 Rs...

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