Question

if the area of circle is 616 cm² find its radius and circumference​

Answer 1

Given :

• Area of circle = 616 cm²

To Find :

• The radius
• The circumference

Solution :

Analysis :

We are given the area of the circle. So from that we can find the radius of the circle. And then by using the circumference formula we will get the circumference of the circle.

Required Formula :

• Area of circle = πr²

• Circumference of circle = 2πr

where,

• r = radius

Explanation :

Let the radius of the circle be “r” cm.

We know that if we are given the area of the circle and is asked to find the radius then our required formula is,

Area of circle = πr²

where,

• π = 22/7
• r = r cm
• Area = 616 cm²

Using the required formula and substituting the required values,

⇒ Area of circle = πr²

⇒ 616 = 22/7 × r²

⇒ 616 × 7/22 = r²

⇒ 4312/22 = r²

⇒ 196 = r²

Square rooting both sides,

⇒ √196 = r

⇒ √[14 × 14] = r

⇒ 14 = r

∴ Radius = 14 cm.

Circumference :

We know that if we are given the radius of the circle and is asked to find the circumference then our required formula is,

Circumference of circle = 2πr

where,

• π = 22/7
• r = 14 cm

Using the required formula and substituting the required values,

⇒ Circumference = 2πr

⇒ Circumference = 2 × 22/7 × 14

⇒ Circumference = 2 × 22 × 2

⇒ Circumference = 4 × 22

⇒ Circumference = 88

∴ Circumference = 88 cm.

Radius of circle is 14 cm.

Circumference of circle is 88 cm.

Answer 2

Correct Question-:

• If the area of circle is 616 cm² .Find its radius and circumference .

AnswEr-:

• $\dag{\underline{\sf{\:Circumference \:of\:Circle \:=\:88cm\:.}}}$
• $\dag{\underline{\sf{\:Radius \:of\:Circle \:=\:14cm\:.}}}$

Explanation-:

• $\frak{Given \:\: -:} \begin{cases} \sf{The\:area\:of\:Circle \:\:is\:= \frak{616cm²}} \end{cases}$

• $\frak{To \:Find\: -:} \begin{cases} \sf{The\:Radius \:Circumference \:of\:Circle \:\:} \end{cases}$

$\dag {\underline {\sf{\large { Solution\:of\:Question-:}}}}$

• $\red{\dag {\underline {\sf{ Area\:of\:Circle\:=\pi \times Radius^{2}}}}}$

• $\underline {\sf{Here-:}}$

• The area of circle is 616 cm² .

• $\sf{\pi= \dfrac{22}{7}}$

• Radius = ??

Now ,

• $\implies{\sf{\:616cm^{2} = \dfrac{22}{7} \times Radius^{2}\:.}}$

• $\implies{\sf{\:\dfrac{616cm \times 7}{22} = Radius^{2}\:.}}$

• $\implies{\sf{\:\dfrac{4312}{22} = Radius^{2}\:.}}$

• $\implies{\sf{\:196 = Radius^{2}\:.}}$

• $\implies{\sf{\:\sqrt {196} = Radius\:[ 14^{2} = \: 196].}}$

• $\implies{\sf{\:14 = Radius\:.}}$

Therefore,

• $\dag{\underline{\sf{\:Radius \:of\:Circle \:=\:14cm\:.}}}$

Now ,

• $\red{\dag {\underline {\sf{ Circumference \:of\:Circle\:=2 \times \pi \times Radius}}}}$

• $\underline {\sf{Here-:}}$

• Radius of Circle = 14 cm

• $\sf{\pi= \dfrac{22}{7}}$

Now ,

• $\implies{\sf{\: 2 \times \dfrac{22}{7} \times 14\:.}}$

• $\implies{\sf{\: 2 \times 22 \times 2\:.}}$

• $\implies{\sf{\: 44 \times 2\:.}}$

• $\implies{\sf{\: 88cm\:.}}$

Therefore,

• $\dag{\underline{\sf{\:Circumference \:of\:Circle \:=\:88cm\:.}}}$

Hence ,

• $\dag{\underline{\sf{\:Circumference \:of\:Circle \:=\:88cm\:.}}}$

• $\dag{\underline{\sf{\:Radius \:of\:Circle \:=\:14cm\:.}}}$

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