Math, asked by hi0, 4 months ago

The circumference of a circular Garden is 66 metre find its area.

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Answered by ujjwal26200
1

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Answered by DüllStâr
73

\text{\Large\underline{\blue{Question:}}}

The circumference of a circular Garden is 66 metre find its area.

\text{\Large\underline{\orange{Diagram:}}}

Kindly see attached picture:D

\text{\Large\underline{\purple{Given:}}}

  • Circumference of a circular Garden = 66 m

\text{\Large\underline{\red{To find:}}}

  • Area of Circular garden

\text{\Large\underline{Answer:}}

So to find area first we should know value of radius.

.°. First let's find radius of Circular garden

We know:

 \bigstar \boxed{ \sf{Circumference \: of \: circle = 2\pi r}}

By using this formula we can find value of radius

: \implies\sf{Circumference \: of \: circle = 2\pi r}

Put value of circumference and pie

: \implies\sf{66= 2 \times\dfrac{22}{7} \times r}

: \implies \sf{}r = 66 \times  \dfrac{1}{2}  \times  \dfrac{7}{22}

: \implies \sf{}r = \cancel{66} {}^{ \: 3}  \times  \dfrac{1}{2}  \times  \dfrac{7}{ \cancel{22} {}^{ \: 1} }

: \implies \sf{}r =  \dfrac{3 \times 7}{2}

: \implies \sf{}r =  \dfrac{21}{2}

: \implies \underline{\boxed{\sf{}r =10.5 \: m}}

Now Finally we can find value of Area by using this formula:

 \bigstar \boxed{ \sf{Area \: of \: circle=\pi r {}^{2} }}

Insert values of pie and radius:

 : \implies\sf{Area \: of \: circle= \dfrac{22}{7}  \times (10.5) {}^{2}  }

 : \implies\sf{Area \: of \: circle= \dfrac{22}{7}  \times 10.5 \times 10.5  } \\

 : \implies\sf{Area \: of \: circle= \dfrac{22}{7}  \times  \dfrac{105}{10}  \times \dfrac{105}{10}  } \\

 : \implies\sf{Area \: of \: circle= \dfrac{22}{ \cancel7 {}^{ \: 1} }  \times  \dfrac{ \cancel{105} {}^{ \: 15} }{10}  \times \dfrac{105}{10}  } \\

 : \implies\sf{Area \: of \: circle= \dfrac{22 \times 15 \times 105}{10 \times 10} } \\

 :\implies\sf{Area \: of \: circle= \dfrac{34,650}{100}} \\

 :\implies\underline {\boxed{\sf{Area \: of \: circle= 346.5m^2}}} \\

_________________________________

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Formulas related to Surface Area and Volume

\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}

And all we are done!

:D

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