Question

If the area of a circle is 154 sq cm. Find the circumference of the circle.

Answer 1

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★GIVEN:-

• $\sf{Area \: \: of \: \: Circle \: = \: 154cm^2}$

★TO FIND:-

• Circumference

★FORMULA USED:-

• $\sf{Area \: \: of \: \: Circle \: = \: \pi {r}^{2} }$

• $\sf{Circumference \: \: of \: \: Circle \: = \: 2\pi \: r }$

★SOLUTION:-

$\sf{Area \: \: of \: \: Circle \: = \: \pi {r}^{2} }$

$: \longrightarrow \sf{154\: = \: \frac{22}{7} \times {r}^{2} }$

$: \longrightarrow \sf{ \frac{154 \times 7}{22} = {r}^{2} }$

$: \longrightarrow \sf{{r}^{2} = \frac{1078}{22} }$

$: \longrightarrow \sf{{r}^{2} = 49}$

$: \longrightarrow \sf{{r}^{2} = {7}^{2} }$

$: \longrightarrow \sf{\: r = \pm \: 7}$

As radius can't be negative. So,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \boxed{ \underbrace{r = 7}}}$

$\sf{Circumference \: \: of \: \: Circle \: = \: 2\pi \: r }$

$\sf{Circumference \: \: of \: \: Circle \: = \: 2 \times \frac{22}{7} \times \: 7 }$

$\sf \purple{Circumference \: \: of \: \: Circle \: = 44cm }$

Answer 2

Answer:

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$\bf\star{\underline{given}}$

• C (o,r ) is a circle

• Area = 154cm²

$\bf\star{\underline{required \: to \: find \: }}$

• radius of circle so that we can find circumference too

• in last we have to find circumference.

$\bf\star{\underline{Solution ~ :- }}$

we know that area of circle is 154cm²

so,

area of circle = πr²

similarly , 154cm² = πr²

154cm² = $\frac{22}{7}$ × r²

= $\frac{154 × 7}{22}$ = r²

= 7 × 7 = r²

= 49 = r²

Radius =$\sqrt{49}$ = 7

• Radius = 7cm

$\bf\star{\underline{Now~circumference~of ~circle}}$

Formula of circumference of circle = 2πr

[ take π = $\frac{22}{7}$ ]

= 2 × $\frac{22}{7}$ × 7

[ radius = 7cm ( given ) ]

$= 2 × \frac{22}{\cancel7}× \cancel7$

= 2 × 22

= 44cm

hence , the circumference of this circle is 44cm