Question

In a rectangular garden of size 110 m by 80 m, a circular lawn
of radius 14 m is provided at its centre. Find the area of the
circular lawn and remaining portion of the garden.​​

Answer 1

Step-by-step explanation:

Given -

Dimensions of rectangular lawn is 110m × 80m

Radius of circular lawn is 14m

To find -

Area of circular lawn and remainig portion.

Formulae used -

Area of rectangle = L × B

Area of circle = πr²

Solution -

In the Question, we are provided with the length and breadth of a rectangular lawn and also with the radius of a circular lawn, and we need to find the area of circle and the remaining portion. For that we will find the area of Rectangular lawn, then the area of circular lawn, then we will subract the area of rectangular lawn from the area of circular lawn, that will give us the area of remaining portion. Let's do it!

According to question -

Length of Rectangular lawn (L) = 110m

Breadth of Rectangular lawn (B) = 80m

Area = L × B

On substituting the values -

$\sf \longrightarrow \: a \: = \: l \: \times \: b \\ \\ \sf \longrightarrow \: a_{(of\: rectangular\:lawn)} \: = 110m \: \times \: 80m \\ \\ \sf \longrightarrow \: a_{(of\: Rectangular\:lawn)} \: = 8800 {m}^{2}$

Similarly -

We will find the area of circular lawn.

Radius of circular lawn (r) = 14m

Area = πr²

On substituting the values -

$\sf \longrightarrow \: a \: = \pi \: {r}^{2} \\ \\ \sf \longrightarrow \: a_{(of\:circular\:lawn)} \: = \dfrac{22}{7} \: \times {(14)}^{2} \\ \\ \sf \longrightarrow \: a_{(of\:circular\:lawn)} \: = \dfrac{22}{7} \: \times \: 196m \\ \\ \sf \longrightarrow \: a_{(of\:circular\:lawn)} \: = 22 \: \times \: 28m \\ \\ \sf \longrightarrow \: a_{(of\:circular\:lawn)} \: = 616m$

Now -

We will find the area of remaining portion, by subtracting the area of rectangular lawn from the area of circular lawn.

$\sf \longrightarrow a_{(of\: remaining\: portion)} \: = \: 8800m \: - 616m \\ \\ \sf \longrightarrow \: a_{(of\:remaining\: portion)} \: = 8184 {m}$

$\therefore$ The area of circular lawn is 616m and the area of remaining portion is 8184m

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Answer 2

$\huge \fbox \colorbox{red}{answer}$

Given :-

Dimensions of rectangular lawn is 110m × 80m

Radius of circular lawn is 14m

To find:-

Area of circular lawn and remainig portion.

Formulae used -

Area of rectangle = L × B

Area of circle = πr²

Solution:-

Length of Rectangular lawn (L) = 110m

Breadth of Rectangular lawn (B) = 80m

Area = L × B

On Substituting value:-

$\begin{gathered} \sf \longrightarrow \: a \: = \: l \: \times \: b \\ \\ \sf \longrightarrow \: a_{(of\: rectangular\:lawn)} \: = 110m \: \times \: 80m \\ \\ \sf \longrightarrow \: a_{(of\: Rectangular\:lawn)} \: = 8800 {m}^{2} \\ \end{gathered}⟶a=l×b⟶a(ofrectangularlawn$

=110m×80m⟶a(ofRectangularlawn)=8800m2

Similarly :-

We will find the area of circular lawn.

Radius of circular lawn (r) = 14m

Area = πr²

On substituting the values :-

$\begin{gathered} \sf \longrightarrow \: a \: = \pi \: {r}^{2} \\ \\ \sf \longrightarrow \: a_{(of\:circular\:lawn)} \: = \dfrac{22}{7} \: \times {(14)}^{2} \\ \\ \sf \longrightarrow \: a_{(of\:circular\:lawn)} \: = \dfrac{22}{7} \: \times \: 196m \\ \\ \sf \longrightarrow \: a_{(of\:circular\:lawn)} \: = 22 \: \times \: 28m \\ \\ \sf \longrightarrow \: a_{(of\:circular\:lawn)} \: = 616m \\ \end{gathered}⟶a=πr2⟶a(ofcircularlawn)=722×(14)2⟶a(ofcircularlawn)=722×196m⟶a(ofcircularlawn)=22×28m⟶a(ofcircularlawn)=616m$

Now:-

We will find the area of remaining portion, by subtracting the area of rectangular lawn from the area of circular lawn.

$\begin{gathered} \sf \longrightarrow a_{(of\: remaining\: portion)} \: = \: 8800m \: - 616m \\ \\ \sf \longrightarrow \: a_{(of\:remaining\: portion)} \: = 8184 {m} \\ \end{gathered}⟶a(ofremainingportion)=8800m−616m⟶a(ofremainingportion)=8184m$

$\bold \pink{ \therefore The \: area \: of \: circular \: lawn \: is \: 616m \: and \: the \: area \: of \: remaining \: portion \: is \: 8184m}$