Question

the diameter of a circular park is 84 meter .On it's outside there a 3.5 meter wide road .Find the cost of constructing the road at rupees 240per meter square

Answer 1

$\red{HEY\:BUDDY!!}$

HERE'S THE ANSWER...

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♠️ So here we go :)

⏺️ radius ( r ) = diameter / 2

=> Radius ( r ) = 84 / 2

=> [ r = 42 m ]

⏺️ Now radius of circle including road

=> Radius ( R ) = 42 + 3.5

=> [ R = 45.5 ]

♠️ Area to be constructed is , ( Area of outer circle ) - ( area of inner circle )

=> $\bold{ Total \:Area\:=\: πR^2 - πr^2}$

=> $\bold{ Total \:Area\:=\: π( R^2 - r^2) }$

=> $\bold{ Total \:Area\:=\: π( {45.5}^2 - {42}^2) }$

=> $\bold{ Total \:Area\:=\:22 / 7 (2070.25 - 1764) }$

=> $\bold{ Total \:Area\:=\:22 / 7 (306.35) }$

=> $\bold{ Total \:Area\:=\: 962.5\: m^2}$

♠️ The road is constructed at the cost of ₹ 240 per m^2 , Now cost for constructing 962.5 m^2 will be ..

=> $\bold{ Cost\:=962.5×240}$

=> $\bold{ Cost\:= 2,31,000 \:Rs}$

▶️ So , total cost required to construct 934 m^2 roal will be [ 2,31,000 ]

HOPE HELPED ✌️

$\red{JAI \:HIND..}$

:)

Answer 2

$Here \: is \: the \: answer \: of \: your \: question$
According to question we have given;

Diameter of circular park = 84 m

Radius of circular park = 84/2 = 42 m

So,

Area of park = π r²

= 22/7 (42 × 42)

= Area of park = 5544 m²

Width of Road = 3.5 m

Total Road = 3.5 + 42 = 45.5 m

Total Area of Road = π r²

= π (Total Road - radius of circular park)

= 22/7 [(45.5 × 45.5) - (42 - 42)]

= 22/7 ( 2070.25 - 1764)

= 22/7 (306.35)

= 962.5 m

Now, the cost of constructing the road is =

Total area of Road × 240 (rupees of constructing the road)

= 962.5 × 240

= 231000 Rs.


So, the ANSWER is

$\textbf{Rs. 231000}$
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