Question

the air of circle 154 cm square finds its diameter and perimeter

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Answer 1

Diameter = 14cm and Perimeter = 44cm

Step-by-step explanation:

Area of a circle = π r² ..... Formula

154 = (22/7) r² .... π = 22/7

r² = (154 x 7) / 22

r² = 49

r = √49

r = 7

Diameter of a circle = 2r .... Formula

= 2 x 7

= 14cm

Perimeter of a circle = 2 π r ..... Formula

= 2 x 22/7 x 7

= 44cm

Answer 2

Answer :-

• Diameter of circle = 14 cm.

• Circumference / Perimeter = 44 cm.

Explanation :-

Given :

• Area of circle = 154 cm.

To Find :

• Diameter and Perimeter of circle.

Solution :

We know that,

$\bigstar \: \underline{\boxed{\sf\red{Area \: of \: Circle = \pi {r}^{2} }}}$

So, Put the values.

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

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

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

$\sf\implies{22 {r}^{2} = 1078}$

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

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

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

$\implies\textsf{\textbf{r = 7 cm }}$

Now, Calculating Diameter of circle.

$\bigstar \: \underline{\boxed{\sf\red{Diameter\: of \: Circle =2r}}}$

$\implies\sf{Diameter\: of \: Circle = 2(7)}$

$\implies\textsf{\textbf{Diameter\: of \: Circle = 14 cm}}$

Now, Calculating Perimeter of circle.

$\bigstar \: \underline{\boxed{\sf\red{Perimeter\: of \: Circle =2\pi r}}}$

$\implies\sf{Perimeter\: of \: Circle = 2 \times \dfrac{22}{7} \times 7 }$

$\implies\sf{Perimeter\: of \: Circle = 2 \times 22 }$

$\implies\textsf{\textbf{Perimeter\: of \: Circle = 44 cm }}$

Therefore,

• Diameter of Circle = 14 cm.

• Circumference of Circle = 44 cm.