Question

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

Answer 1

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.

Answer 2

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

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

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

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

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