Question

If area of circle is 44 cm. Then find its circumference.

Answer 1

Step-by-step explanation:

Question:-

If the area of the circle is 44cm,then find its circumference.

Answer:-

Given :-

• The given figure is a circle.

• The area of the circle is 44cm.

To find :-

The circumference of the circle

Process :-

We all know that :-

$⇒Area = \pi {r}^{2}$

∴ Putting the above value in the equation:-

$⇒ Area =\pi {r}^{2} \\ \\ ⇒ 44 =3.15 \times {r}^{2} \\ \\ ⇒ {r}^{2} ×3.15=44 \\ \\ ⇒ {r}^{2} = \frac{44}{3.15} \\ \\ ⇒ {r}^{2} =1 44× \frac{100}{315} \\ \\ ⇒ {r}^{2} = 13.96 \\ \\ ⇒r = \sqrt{13.96} \\ \\ ⇒r = 3.7$

∴ We can see that the radius of the circle is 3.7cm.

Then,the circumference of the circle:-

$⇒ Circumference = 2\pi \: r$

Putting the value of radius in the equation:-

$⇒ Circumference = 2×\pi×3.7 \\ \\ ⇒ Circumference = 2×3.15×3.7 \\ \\ ⇒ Circumference = 23.31 \: cm$

Thus,we can conclude that the circumference of the circle is 23.31cm.

★ More to know

( Is provided in the attachment )

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Answer 2

Digram:

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3.74\ cm}\end{picture}$

Correct Question:

If area of circle is 44 cm². Then find its circumference.

Given:

• Area of Circle = 44 cm²

To find:

• circumference of Circle

Solution:

To find circumference first we should know value of radius of circle

we know:

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

By using this formula we can find value of Area of Circle .

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

$\dashrightarrow \: \sf{}44= \dfrac{22}{7} \times {r}^{2}$

$\dashrightarrow \: \sf{}\dfrac{22}{7} \times {r}^{2} = 44$

$\dashrightarrow \: \sf{}{r}^{2} = 44 \times \dfrac{7}{22}$

$\dashrightarrow \: \sf{}{r}^{2} = 2 \times 2 \times 11 \times \dfrac{7}{2 \times 11}$

$\dashrightarrow \: \sf{}{r}^{2} = 2 \times\cancel 2 \times \cancel{11} \times \dfrac{7}{\cancel2 \times\cancel{ 11}}$

$\dashrightarrow \: \sf{}{r}^{2} = 2 \times7$

$\dashrightarrow \: \sf{}{r}^{2} = 14$

$\dashrightarrow \: \sf{}{r} = \sqrt{14}$

$\dashrightarrow \: \sf{}{r} = 3.74 \: cm \: \: \{approx \}$

Finally Let's find circumference of circle .

we know:

$\bigstar \boxed{ \rm{circumference \: of \: circle =2\pi{}r}}$

By using this formula we can find value of circumference of Circle

$\leadsto \sf{}circumference \: of \: circle =2\pi{}r$

$\leadsto \sf{}circumference \: of \: circle =2 \times \dfrac{22}{7} \times 3.74$

$\leadsto \sf{}circumference \: of \: circle =2 \times \dfrac{22}{7} \times 3.74$

$\leadsto \sf{}circumference \: of \: circle =\dfrac{22 \times 2 \times 3.74}{7}$

$\leadsto \sf{}circumference \: of \: circle =\dfrac{164.56}{7}$

$\leadsto \underline{ \boxed{ \sf{}circumference \: of \: circle =23.5 \: cm}}$

$\therefore \underline{\textsf{circumference \: of \: circle = \textbf{23.5 \: cm}(approx)}}$

know more:

$\textbf{Formulas of area :}$

$\boxed{\begin {minipage}{9cm}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {minipage}}$