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The area of a circular play groud is 616...

The area of a circular play groud is 616 `m^(2)`. A path of width 3 m is laid around and outside of it. Find the cost of levelling the path at the rate of Rs.14 per square metre.

A

Rs.4093

B

Rs.4090

C

Rs.4000

D

Rs.4000

Text Solution

Verified by Experts

The correct Answer is:
D
Given that area of the circular field `=616m^(2)`
`rArr pir^(2)=616`
`rArr(22)/(7)xxr^(2)=616`
`rArr r^(2)=(616xx7)/(22)=28xx7`
`rArr r = 2xx7=14m`
`therefore` The outer radius (R) of the circular path
`=14+3=17m`
`therefore "Area of the path"=pi(R^(2)-r^(2))=pi(17^(2)-14^(2))`
`=93xx(22)/(7)`
`therefore"The cost of levelling the path"=93xx(22)/(7)xx14`
= Rs. 4091
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