Question

A 7m wide path is to be constructed all around,and outside pf a circular field of diameter 112m.Find the cost of constructing the path at ₹50.

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Answer 1

Appropriate Question :-

A 7m wide path is to be constructed all around, and outside of a circular field of diameter 112m. Find the cost of constructing the path at ₹50 per square meter.

$\large\underline{\sf{Solution-}}$

Let assume that r represents the radius of inner circle and R represents the radius of outer circle.

So, given that,

Diameter of inner circle = 112 m

So, radius of inner circle, r = 56 m

Width of path, h = 7 m

So, Radius of outer circle, r = R + h = 56 + 7 = 63 m

So,

$\rm \: Area_{(path)} = \pi \: {R}^{2} \: - \: \pi \: {r}^{2}$

$\rm \: Area_{(path)} = \pi \: ( {R}^{2} \: - \: {r}^{2})$

$\rm \: Area_{(path)} = \dfrac{22}{7} \times ( {63}^{2} \: - \: {56}^{2})$

$\rm \: Area_{(path)} = \dfrac{22}{7} \times (63 + 56)(63 - 56)$

$\rm \: Area_{(path)} = \dfrac{22}{7} \times 119 \times 7$

$\rm \: Area_{(path)} = 22 \times 119$

$\rm\implies \:\rm \: Area_{(path)} = 2618 \: {m}^{2}$

Now, given that

$\rm \: Cost\:of\:construction\:of \: {1 \: m}^{2} = 50$

So,

$\rm \: Cost\:of\:construction\:of \: {2618 \: m}^{2} = 2618 \times 50$

$\rm \: Cost\:of\:construction\:of \: {2618 \: m}^{2} = 130900$

Hence,

Cost of construction of the path = ₹ 1, 30, 900

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$

Answer 2

PROVIDED INFORMATION :-

• A 7m wide path is to be constructed all around,and outside pf a circular field of diameter 112m

TO FIND :-

• Find the cost of constructing the path at ₹50 = ?

SOLUTION :-

Radius of inner circle = 112/ 2 = 56

Radius of outer circle = 56 + 7 =63 m

Area of path

Area of outer circle - Area of inner circle

= π × 63² - π × 56²

= π ( 63² - 56²) = 22/7 (63 + 56)(63 - 56)

= 22/7 × 119 × 7 = 22 × 119 = 2618 m²

Cost of constructing the path

= (2618 × 50) = 130900