Question

a road which is 3m. wide sorrunds a circular park whose radius is 37 m find the cost of construction of road at the rate of rs 20 per square metre​

Answer 1

Diagram is given in attachment

$\red{radius \: of \: bigger \: circle }\\ = 37 + 3 = 40m \\ area \: of \: bigger \: circle = \pi(40) {}^{2} \\ = \pi(1600) \\ = 3.14(1600) = 5024m {}^{2}$

$\blue{radius \: of \: smaller \: circle} \\ = 37cm \\ area \: of \: smaller \: circle \\ = \pi(37) {}^{2} \\ = 3.14(1369) \\ = 4298 .66$

$\green{area \: of \: road \: = area \: of \: bigger \: circle - area \: of \: smaller \: circle} \\ = 5024 - 4298.66 = 725.34m {}^{2}$

ratev=20Rs /square metre

$\orange{total \: cost} = 20 \times 725.34 \\ \pink{ \approx 14506.8rs}$

hope it helps

Answer 2

Answer:

Radius of park x =84/2 =42 m

radius of outer circle y = 42 +3.5 =45.5m

area of road=

$\pi( {y}^{2} - {x}^{2} ) \\ \pi( {45.5}^{2} - {42}^{2} ) \\ \frac{22}{7} (2070.25 - 1764) \\ \frac{22}{7} \times 306.25 \\ 962.25 {m}^{2}$

cost of construction =20×962.25

= 19,245 ₹

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