Question

A circular plot has a radius of 42m .A 3.5 m wide road runs on the inside of the plot around it. Find the area of the road. Also find the cost of paving the road at rupees 45 per metre square

Answer 1

it is the right answer that is 39847.5rupee

Answer 2

$Radius \: of \: a \: circular \: plot (R) = 42 \:m$

$Width \:of \:the \: road \: inside \:of \:the \\plot (w) = 3.5 \:m$

$Radius \: of \:the \: inner \:circle (r) = R - w \\= 42 \:m - 3.5\:m \\= 38.5 \:m$

$i ) Area \: of \:the \:road (A) \\= Area \:of \: outer \:circle - Area \:of \:the \:inner \:circle \\= \pi R^{2} - \pi r^{2} \\=\pi( R^{2} - r^{2} ) \\= \pi ( R+r)(R-r) \\= \pi(R+r) w \\= \frac{22}{7} \times ( 42 + 3.5) \times 3.5 \\= 22 \times 45.5 \times 0.5 \\= 500.5 \:m^{2}\: ---(1)$

$ii ) Cost \:of\: paving \: 1 \:m^{2} \: road = Rs \:45$

$Cost \:of\: paving \: 500.5 \:m^{2} \: road \\= 45 \times 500.5 \\= Rs \: 22522.50\: --(2)$

Therefore.,

$\red{Area \: of \:the \:road } \green {= 500.5 \:m^{2}}$

$\red{Cost \:of\: paving \: 500.5 \:m^{2} \: road}\\\green {= Rs \: 22522.50}$

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