Question

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This is the question to check your mathematics. Please help !!!

A grassy park of length 20 m and breadth 15 m is there. There is a circular pond of radius 7 m at the centre of it. Find the cost of cementing the park except the pond, at the rate of Rs. 15 per sq. m. Assume that there is no place left except pond. Give the correct answer.

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Answer 1

Answer :-

$\: \\ \: \boxed{\boxed{\rm{\mapsto \: \: \: \orange{Firstly \: let's \: understand \: the \: concept \: used \: :-}}}}$

Here the concept of Area of Rectangle and Area of Circle has been used. We see that the dimensions of the Rectangular Park has been given. We can find its area and then we can subtract the area of pond from it. The area left can be multiplied with the rate and then find the total cost.

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★ Formula Used :-

$\:\: \\\: \large{\boxed{\boxed{\sf{Area \: of \: Rectangle_{(park)} \: = \: \bf{\blue{Length(L) \: \times \: Breadth(B)}}}}}}$

$\:\: \\\: \large{\boxed{\boxed{\sf{Area \: of \: Circle_{(pond)} \: = \: \bf{\blue{\pi r^{2}}}}}}}$

$\:\: \\ \: \large{\boxed{\boxed{\sf{Area \: to \: be \: Cemented \: = \: \bf{\blue{Area \: of \: Park \: - \: Area \: of \: Pond}}}}}}$

$\: \: \\ \: \large{\boxed{\boxed{\sf{Total \: cost \: of \: Cementing \: = \: \bf{\blue{Area \: to \: be \: Cemented \: \times \: Rate_{(in \: per \: m^{2})}}}}}}}$

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★ Solution :-

Given,

» Length of the Rectangular Plot = 20 m

» Breadth of the Rectangular Plot = 15 m

» Radius of the Circular Pond = 7 m

» Rate of Cementing per m = Rs. 15

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~ For the Area of Park :-

$\:\: \\ \qquad\: \large{\sf{\rightarrow \: \: \: Area \: of \: Rectangle_{(park)} \: = \: \bf{Length(L) \: \times \: Breadth(B)}}}$

$\:\: \\ \qquad\: \large{\sf{\rightarrow \: \: \: Area \: of \: Rectangle_{(park)} \: = \: \bf{20 \: m \: \times \: 15 \: m \: \: = \: \: \underline{\underline{300 \: m^{2}}}}}}$

$\: \\ \: \large{\boxed{\boxed{\tt{Area \:\; of \:\; Park \:\; = \; \bf{\red{300 \: m^{2}}}}}}}$

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~ For the Area of Pond :-

$\:\: \\ \qquad \: \large{\sf{\rightarrow \: \: \: Area \: of \: Circle_{(pond)} \: = \: \bf{\pi r^{2}}}}$

$\:\: \\ \qquad \: \large{\sf{\rightarrow \: \: \: Area \: of \: Circle_{(pond)} \: = \: \bf{\dfrac{22}{\cancel{7}} \: \times \: (7)^{\cancel{2}}}}}$

$\:\: \\ \qquad \: \large{\sf{\rightarrow \: \: \: Area \: of \: Circle_{(pond)} \: = \: \bf{22 \: \times \: 7 \: \: = \: \: \underline{\underline{154 \: m^{2}}}}}}$

$\: \\ \: \large{\boxed{\boxed{\tt{Area \:\; of \:\; Pond \:\; = \; \bf{\red{154 \: m^{2}}}}}}}$

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~ For the Area to be Cemented :-

$\:\: \\ \qquad \: \large{\sf{\longrightarrow \: \: \: Area \: to \: be \: Cemented \: = \: \bf{Area \: of \: Park \: - \: Area \: of \: Pond}}}$

$\:\: \\ \qquad \: \large{\sf{\longrightarrow \: \: \: Area \: to \: be \: Cemented \: = \: \bf{300 \: m^{2} \: - \: 154 \: m^{2} \: = \: \: \underline{\underline{146 \: m^{2}}}}}}$

$\: \\ \: \large{\boxed{\boxed{\tt{Area \:\; to \:\; be \:\; Cemented \:\; = \; \bf{\red{146 \: m^{2}}}}}}}$

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~ For the Total Cost of Cementing :-

$\: \\ \: \qquad \: \large{\sf{\longmapsto \: \: \: Total \: cost \: of \: Cementing \: = \: \bf{Area \: to \: be \: Cemented \: \times \: Rate_{(in \: per \: m^{2})}}}}$

$\: \\ \: \qquad \: \large{\sf{\longmapsto \: \: \: Total \: cost \: of \: Cementing \: = \: \bf{146 \: m^{2} \: \times \: 15 \: per \: m^{2} \: \: = \: \: \underline{\underline{Rs.\: 2190}}}}}$

$\: \\ \: \large{\boxed{\boxed{\tt{Total \:\; cost \:\; of \:\; Cementing \:\; = \; \bf{\red{Rs. \: 2190}}}}}}$

$\: \: \\ \large{\underline{\underline{\rm{\leadsto \: \: \: Thus, \: total \: cost \: of \: cementing \: the \: park \: is \: \: \boxed{\bf{Rs. \: 2190}}}}}}$

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$\: \\ \: \quad \large{\underline{\mapsto{\sf{\blue{Evaluation \: \: from \: \: the \: \: Figure}}}}}$

From figure we see that, DEFG is the rectangular grassy park. There is a pond in the centre.

• DE = length of the park = 20 m

• GF = length of the park = 20 m

• DG = breadth of the park = 15 m

• EF = breadth of the park = 15 m

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$\: \qquad \large{\underbrace{\underbrace{\sf{\purple{More \: formulas \: to \: know \: :-}}}}}$

• Area of Square = (Side)²

• Area of Triangle = ½ × Base × Height

• Perimeter of Square = 4 × Side

• Perimeter of Rectangle = 2πr

• Perimeter of Triangle = Sum of the sides

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Answer 2

Solution :

Cost of cementing the park except the pond is ₹2190 .

Step by step explanation :

Let the Area of park and pond be $\sf\:A_1\:and\:A_2$ and Area of cementing surface be A .

Dimensions of Park

• Length = 20m
• Breadth = 15 m

$\rm\:A_1=length\:\times\:breadth$

Put the given values

$\sf\implies\:A_1=20\times15$

$\sf\implies\:A_1=300m^2$

Dimensions of circular Pond

• Radius of pond , r= 7 cm

$\rm\:A_2=\pi\:r^2$

$\sf\implies\:A_2=\dfrac{22}{7}\times(7)^2$

$\sf\implies\:A_2=\dfrac{22}{7}\times7\times7$

$\sf\implies\:A_2=22\times7$

$\sf\implies\:A_2=154m^2$

We have to find the cost of cementing the park except the pond, at the rate of Rs. 15 per sq. m.

Area of cementing

$\rm\:A=A_1-A_2$

$\sf\implies\:A=(300-154)m^2$

$\sf\implies\:A=146m^2$

Rate of cementing = ₹15 m²

Thus,

Cost of cementing =₹15× 146=₹2190