Question

The area of a circle is 616cm square. Find its circumference take π = 22/7

Answer 1

Question

The area of a circle is 616 cm². Find its circumference take π = 22/7

Solution

Given :-.

• Area of circle = 616 cm²

Find :-

• Circumference of circle

Explanation

Important Formula

★ Area of circle = πr²

★ Circumference of circle = 2πr

So, Now

==> Area of circle = πr²

==> 616 = 22/7 × r²

==> r² = 616 × 7/22

==> r² = 28 × 7

==> r = √(7 × 7 × 2 ×2)

==> r = 7 × 2

==> r = 14

Since,

• Radius of circle be = 14 cm

__________________________

Now, Calculate circumference of circle

==> Circumference of circle = 2πr

Keep Value of r & π

==> Circumference of circle = 2 × 22/7 × 14

==> Circumference of circle = 2 × 22 × 2

==> Circumference of circle = 88 cm

Hence

• Circumference of circle be = 88 cm

___________________

Answer 2

GIVEN:

• Area of circle = 616 cm²

TO FIND:

• What is the Circumference of the circle ?

SOLUTION:

We have given that the area of the circle is 616 cm²

Take π = 22/7

According to question:-

✫ Area of circle = πr² ✫

Let the radius of the circle be 'r' cm

On putting the values in the formula, we get

$\rm{\implies 616 = \dfrac{22}{7} \times {r}^{2}}$

$\rm{\implies 616 \times 7 = 22 \times {r}^{2}}$

$\rm{\implies 4312 = 22 \times {r}^{2}}$

$\rm{\implies {r}^{2} = \cancel\dfrac{ 4312}{22}}$

$\rm{\implies {r}^{2} = 196}$

$\rm{\implies r = \sqrt{196}}$

$\bf{\implies r = 14 \: cm}$

❝ Radius of the circle is 14 cm ❞

Now, we have to find the circumference of the circle

✫ Circumference of circle = 2πr ✫

On putting the values in the formula, we get

$\rm{\implies Circumference = 2 \times \dfrac{22}{7} \times 14}$

$\rm{\implies Circumference = 2 \times \dfrac{22}{\cancel{7}} \times \cancel{14}}$

$\rm{\implies Circumference = 2 \times 22 \times 2}$

$\bf{\implies \star \:Circumference = 88 \: cm\: \star }$

❝ Hence, the circumference of the circle is 88 cm ❞

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VERIFICATION:

Put the values in the formula of circumference of circle

➠ $\bf{ 88 = 2 \pi r}$

➠ $\bf{ 88 = 2 \times \dfrac{22}{7} \times 14}$

➠ $\bf{ 88 = 2 \times \dfrac{22}{\cancel{7}} \times \cancel{14}}$

➠ $\bf{ 88 = 2 \times 22 \times 2}$

➠ $\bf{ 88 = 88}$

$\bf{ L.H.S. = R.H.S.}$

VERIFIED....