Question

if the circumference of a circle is 154m find it's radius also also,find the area of the circle
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Answer 1

Question :-

If the circumference of a circle is 154 m . Find its radius also and area of the circle ?

Answer :-

Given :-

Circumference of a circle = 154 meters

Required to find :-

• Radius of the circle

• Area of the circle

Formulae used :-

$\large{\leadsto{\boxed{\rm{ Perimeter \; of \; a \; circle = 2 \pi r }}}}$

$\large{\leadsto{\boxed{\rm{ Area \; of \; a \; circle = \pi {r}^{2}}}}}$

Solution :-

Given that :-

Circumference of the circle = 154 meters .

He asked us to find the radius and area of the circle .

So,

Let's take ,

The radius of circle = " x " meters

So,

Using the formula ,

$\large{\leadsto{\boxed{\rm{ Perimeter \; of \; a \; circle = 2 \pi r }}}}$

Now substitute the required values

( Taking π value as 22/7 )

Hence ,

$\longrightarrow{\mathsf{154 = 2 \times \dfrac{22}{7} \times x }}$

$\longrightarrow{\mathsf{ 154 = \dfrac{44}{7}x }}$

Interchange the terms on both sides

$\longrightarrow{\mathsf{ \dfrac{44}{7}x = 154 }}$

$\longrightarrow{\mathsf{ x = 154 \div \dfrac{44}{7}}}$

$\longrightarrow{\mathsf{ x = 154 \times \dfrac{7}{44}}}$

$\longrightarrow{\mathsf{ x = \dfrac{1078 }{44}}}$

$\implies{\mathsf{x = 24.5 \; meters }}$

Hence,

$\boxed{\large{\tt{ Radius \; of \; the \; circle = 24.5 \; meters }}}$

However,

Now let's find the area of the circle .

To find the area of the circle we should use a formula .

The formula is ,

$\large{\leadsto{\boxed{\rm{ Area \; of \; a \; circle = \pi {r}^{2}}}}}$

So,

Using this formula we can find the area of the circle .

Substitute the respective values

( Value of π = 22/7 )

$\Rightarrow{\tt{ Area \; of \; circle \; = \dfrac{22}{7} \times { 24.5 }^{2}}}$

$\Rightarrow{\tt{ Area \; of \; circle = \dfrac{ 22 }{7} \times 24.5 \times 24.5 }}$

$\Rightarrow{\tt{ Area = \dfrac{13205.5 }{7}}}$

$\implies{\tt{ Area = 1,886.5 {m}^{2}}}$

Therefore,

$\boxed{\large{\mathsf{ Area \; of \; the \; circle = 1886.5 {m}^{2}}}}$

Points to remember :-

1. It is important to remember the formulae .

So,

$\large{\leadsto{\boxed{\rm{ Perimeter \; of \; a \; circle = 2 \pi r }}}}$

$\large{\leadsto{\boxed{\rm{ Area \; of \; a \; circle = \pi {r}^{2}}}}}$

2. The word circumference and perimeter both have the same meaning .

3. If we take the value of pi as 3.14 then the area will be as 1885.75 m² which on whole can be taken as 1886.5 m²

4. Refer to the attachment .

Answer 2

Answer:

Step-by-step explanation:

Given :-

Circumference of circle = 154 m

To Find :-

Area of circle

Formula to be used :-

Circumference of circle = 2πr

Ares of circle = πr²

Solution :-

Putting all the values, we get

Circumference of circle = 2πr

⇒ 154 = 2πr

⇒ 154 = 2 × 22/7 × r

⇒ 49/ 2 = r

⇒ r = 24.5 m

Now, Area of circle

Ares of circle = πr²

⇒ Ares of circle = 22/7 × 24.5 × 24.5

⇒ Ares of circle = 1886.5 m²

Hence,  the area of the circle  is 1886.5 m².