Question

A rectangular ground is 60 m long and 22 m broad. In the
middle of the ground there is a circular pond of radius 14
m. Find the cost of putting grass on the remaining portion
at the rate of 60 per sqm.​

Answer 1

Answer :-

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

Here the concept of Areas of Rectangle and Areas of Circle is used. We see that a Rectangular Ground is given and in which there is a circular pond. Here we can't grass over the pond. So we need to calculate the area of ground and pond first. Then we will subtract the area of pond from ground and we will multiply the left area with the rate.

Let's do it !!

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★ Formula Used :-

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

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

$\: \\ \large{\boxed{\boxed{\sf{Area \: to \: be \: Grassed \: = \: \bf{Area \: of \: Ground \: - \: Area \: of \: Pond}}}}}$

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

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★ Question :-

A rectangular ground is 60 m long and 22 m broad. In the middle of the ground there is a circular pond of radius 14 m. Find the cost of putting grass on the remaining portion at the rate of 60 per sq m.

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★ Solution :-

Given,

» Length of the rectangular ground = L = 60 m

» Breadth of the rectangular ground = B = 22 m

» Radius of the pond = r = 14 m

» Rate of grassing in per m² = ₹ 60

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~ For the Area of Ground :-

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

$\: \\ \qquad \large{\sf{:\longrightarrow \: \: \: Area \: of \: Rectangle_{(ground)} \: = \: \bf{60 \: m \: \times \: 22 \: m \: \: = \: \: \underline{\underline{1320 \: m^{2}}}}}}$

$\: \\ \large{\boxed{\boxed{\tt{Area \;\; of \;\; Rectangular\;\; ground\;\; = \; \bf{1320 \: \: m^{2}}}}}}$

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~ For the Area of Pond :-

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

$\: \\ \qquad \large{\sf{:\longrightarrow \: \: \: Area \: of \: Circle_{(pond)} \: = \: \bf{\dfrac{22}{7} \: \times \: (14)^{2}}}}$

$\: \\ \qquad \large{\sf{:\longrightarrow \: \: \: Area \: of \: Circle_{(pond)} \: = \: \bf{\dfrac{22}{\cancel{7}} \: \times \: \cancel{196} \: m^{2} \: \: = \: \: \underline{\underline{616 \: m^{2}}}}}}$

$\: \\ \large{\boxed{\boxed{\tt{Area \;\; of \;\; Circular \;\; Pond\;\; = \; \bf{616 \: \: m^{2}}}}}}$

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~ For the Area to be Grassed :-

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

$\: \\ \qquad \large{\sf{:\longrightarrow \: \: \: Area \: to \: be \: Grassed \: = \: \bf{1320 \: m^{2} \: - \: 616 \: m^{2} \: \: = \: \: \underline{\underline{704 \: m^{2}}}}}}$

$\: \\ \large{\boxed{\boxed{\tt{Area \;\; to \;\; be \;\; Grassed\;\; = \; \bf{704 \: \: m^{2}}}}}}$

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~ For the Total Cost of Grassing :-

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

$\: \\ \qquad \large{\sf{:\Longrightarrow \: \: \: Total \: cost \: of \: Grassing \: = \: \bf{Rs.\: 60 \: per \: m^{2} \: \times \: 704 \: m^{2} \: \: = \: \: \underline{\underline{Rs.\: 42240}}}}}$

$\: \: \\ \large{\underline{\underline{\rm{\mapsto \: \: \: Thus, \; total \; cost \; of \; Grassing \; in \; the \; remaining \; portion \; is \;\; \boxed{\bf{Rs.\:\: 42,240}}}}}}$

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$\: \large{\underbrace{\underbrace{\sf{More \; to \; know \; :-}}}}$

• Area of Square = (Side)²

• Area of Triangle = ½ × Base × Height

• Area of Parallelogram = Base × Height

• Perimeter of Rectangle = 2(Length + Breadth)

• Perimeter of Circle = 2πr

• Perimeter of Square = 4 × Side

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Answer 2

Given,

A rectangular ground is 60 m long and 22 m broad. In the  middle of the ground there is a circular pond of radius 14  m.

To find :

Find the cost of putting grass on the remaining portion  at the rate of 60 per sqm.​

Solution :

Given, length and breadth of rectangular ground are 60m and 22m

∴ Area of rectangular garden = 60 * 22

∴ Area of rectangular garden = 1320 m²

Now, radius of circular pond = 14 m

∴ Area of circular pond = 22/7 * 14²

⇒ Area of circular pond = 22/7 * 196

⇒ Area of circular pond = 22 * 28

∴ Area of circular pond = 616 m²

Now area of remaining portion :

⇒ Area of remaining portion = Area of ground - Area of pond

⇒ Area of remaining portion = 1320 - 616

⇒ Area of remaining portion = 704 m²

Now we have, rat of putting grass = Rs. 60/m²

∴ Cost of putting grass = Area * Rate

⇒ Cost of putting grass = 704 * 60

⇒ Cost of putting grass = Rs. 42240

Therefore,

Cost of putting grass on remaining portion = Rs. 42240