Question

if the area of a circle is 616 CM square find its circumference ​

Answer 1

Answer:

circumference of the circle = 88cm

Step-by-step explanation:

Answer 2

Answer:

Circle :

Let us know some information about circle and it's parts :

↝ A circle is defined as the locus of a point which moves in a plane such its distance from a fixed point in that plane is always constant.

Parts of Circle :

• Arc - It is basically the connected curve of a circle.
• Sector - A region bounded by two radii and an arc.
• Segment - A region bounded by a chord and an arc lying between the chord’s endpoints. It is to be noted that segments do not contain the centre.
• Centre - It is the midpoint of a circle.
• Chord- A line segment whose endpoints lie on the circle.
• Diameter- A line segment having both the endpoints on the circle and is the largest chord of the circle.
• Radius - A line segment connecting the centre of a circle to any point on the circle itself.
• Secant - A straight line cutting the circle at two points. It is also called an extended chord.
• Tangent - A coplanar straight line touching the circle at a single point.

$\begin{gathered}\end{gathered}$

Diagram :

Rough diagram of circle :

$\setlength{\unitlength}{1mm}\begin{picture}(50,55)\linethickness{0.4mm}\qbezier(45,30)(45,30)(5,30)\qbezier(25.000,10.000)(33.284,10.000)(39.142,15.858)\qbezier(39.142,15.858)(45.000,21.716)(45.000,30.000)\qbezier(45.000,30.000)(45.000,38.284)(39.142,44.142)\qbezier(39.142,44.142)(33.284,50.000)(25.000,50.000)\qbezier(25.000,50.000)(16.716,50.000)(10.858,44.142)\qbezier(10.858,44.142)( 5.000,38.284)( 5.000,30.000)\qbezier( 5.000,30.000)( 5.000,21.716)(10.858,15.858)\qbezier(10.858,15.858)(16.716,10.000)(25.000,10.000)\multiput(5,30)(20,0){3}{\circle*{1}}\end{picture}$

$\begin{gathered}\end{gathered}$

Given :

• ➠ Area of circle = 212 cm².

$\begin{gathered}\end{gathered}$

To Find :

• ➠ Circumference of circle

$\begin{gathered}\end{gathered}$

Solving Process :

↝ To solve this question firstly let's find the radius of circle by using formula, we have to put the values.

↝ Then we have to find the circumference of circle by using formula, just have to put the values.

$\begin{gathered}\end{gathered}$

Using Formulas :

$\longrightarrow\underline{\boxed{\sf{A=\pi{r}^2}}}$

$\longrightarrow\underline{\boxed{\sf{C=2\pi r}}}$

Where :-

• ➠ A = Area
• ➠ π = 22/7
• ➠ r = radius
• ➠ C = circumference

$\begin{gathered}\end{gathered}$

Solution :

Finding the radius of circle by substituting the values in the formula :-

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

${\dashrightarrow{\sf{616= \dfrac{22}{7} \times {r}^2}}}$

${\dashrightarrow{\sf{{r}^2} = 616 \times \dfrac{7}{22}}}$

${\dashrightarrow{\sf{{r}^2} = \dfrac{616 \times 7}{22}}}$

${\dashrightarrow{\sf{{r}^2} = \dfrac{4312}{22}}}$

${\dashrightarrow{\sf{{r}^2} = \cancel{\dfrac{4312}{22}}}}$

${\dashrightarrow{\sf{{r}^2} =196}}$

${\dashrightarrow{\sf{r = \sqrt{196} }}}$

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

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

${\bigstar \: {\underline{\boxed{\sf{\red{Radius = 14 \: cm }}}}}}$

∴ The radius of circle is 14 cm.

$\rule{300}{1.5}$

Now, finding the circumference of circle by substituting the values in the formula :-

${\dashrightarrow{\sf{Circumference=2\pi r}}}$

${\dashrightarrow{\sf{Circumference = 2 \times \dfrac{22}{7} \times 14}}}$

${\dashrightarrow{\sf{Circumference = \dfrac{2 \times 22 \times 14}{7}}}}$

${\dashrightarrow{\sf{Circumference = \dfrac{44\times 14}{7}}}}$

${\dashrightarrow{\sf{Circumference = \dfrac{616}{7}}}}$

${\dashrightarrow{\sf{Circumference = \cancel{\dfrac{616}{7}}}}}$

${\dashrightarrow{\sf{Circumference =88 \: cm}}}$

${\bigstar \: {\underline{\boxed{\sf{\red{Circumference =88 \: cm}}}}}}$

∴ The circumference of circle is 88 cm.

$\begin{gathered}\end{gathered}$

Diagram :

Diagram of circle with radius :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf{\large{14\ cm}}}\end{picture}$

$\begin{gathered}\end{gathered}$

Learn More :

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

${\underline{\rule{220pt}{2.5pt}}}$