Science, asked by ghostrider34, 4 months ago

if the area of a circle is 154 m2 find its radius. also find the circumference of the circle​

Answers

Answered by Mysterioushine
22

Given :

  • Area of circle = 154 m²

To Find :

  • Radius and circumference of the circle

Solution :

Area of circle is given by ,

 \\  \star \: {\boxed{\purple{\sf{Area_{(circle)} = \pi {r}^{2} }}}} \\  \\

Where ,

  • r is radius of circle

We have Area of circle as 154 m².

 \\   : \implies \sf \: 154 =  \dfrac{22}{7}  \times  {r}^{2}  \\  \\

 \\   : \implies \sf \: 154 \times 7 = 22 \times  {r}^{2}  \\  \\

 \\   : \implies  \sf \: 1078 = 22 \times  {r}^{2}  \\  \\

 \\  :  \implies \sf \: \dfrac{1078}{22}  =  {r}^{2}  \\  \\

 \\   : \implies  \sf \:  {r}^{2}  = 49 \\  \\

 \\  :  \implies \sf \: r =  \sqrt{49}  \\  \\

 \\   : \implies{\underline{\boxed{\pink{\mathfrak{r = 7 \: m}}}}}  \: \bigstar \\  \\

So , Radius of the circle whose area is 154 m² is 7 m.

Now , Circumference of a circle is given by ;

 \\  \star \: {\boxed{\purple{\sf{circumference_{(circle)} = 2\pi r}}}} \\  \\

Where ,

  • r is radius of circle

Substituting the values we have ,

 \\  :  \implies \sf \: Circumference_{(circle)} = 2 \times  \frac{22}{7}  \times 7 \\  \\

 \\  :  \implies \sf \: Circumference_{(circle)} = 2 \times 22 \\  \\

 \\   : \implies{\underline{\boxed{\pink{\mathfrak{circumference_{(circle)} = 44 \: m}}}}}  \: \bigstar \\  \\

Hence ,

  • The radius and circumference of a circle whose area is 154 m² is 7 m and 44 m.
Answered by Anonymous
10

Answer:

Given :-

Area of circle = 154 m²

To Find :-

  1. Radius
  2. Circumference

Solution :-

As we know that

 \huge \tt \: Area( \circ) = \pi r {}^{2}

 \tt \: 154 =  \dfrac{22}{7}  \times  {r}^{2}

 \tt \: 154 \times 7 = 22 \times r {}^{2}

  \tt \: 1078 = 22 \times  {r}^{2}

 \tt \:  \dfrac{1078}{22}  =  {r}^{2}

 \tt \cancel \dfrac{1078}{22} =  {r}^{2}

 \tt \: 49 =  {r}^{2}

 \tt \pink{  \sqrt{49}  = r}

 \tt \red{7 = r}

Hence :-

Radius is 7 cm

 \tt \: circumference \:  = 2\pi r

 \tt \: circumference \:  = 2 \times  \dfrac{22}{7}  \times 7

 \tt \: circumference \:  = 2 \times   \cancel\dfrac{22}{7}  \cancel{ \times 7}

 \tt \: circumference \:  = 2 \times  22 = 44 cm

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