Question

7. Find the circumferen
he circumference of a circle whose area is
4 times the area of a circle with diameter 21 cm​

Answer 1

Solution:

Given:

=> Diameter of 1st circle = 21 cm

=> Radius of 1st circle = 21/2 cm

=> Area of 2nd circle is 4 times the area of 1st circle

To Find:

=> Circumference of the circle.

Formula used:

$\sf{\implies Area\;of\;circle=\pi r^{2}}$

$\sf{\implies Circumference\;of\;circle=2\pi r}$

Now, we will find area of 1st circle,

$\sf{\implies Area\;of\;circle=\pi r^{2}}$

$\sf{\implies \dfrac{22}{7}\times (10.5)^{2}}$

$\sf{\implies \dfrac{22}{7}\times 110.25}$

$\sf{\implies 346.5\;cm^{2}}$

We know that area of 2nd circle is 4 times the area of 1st circle.

So, area of 2nd circle = 4 × 346.5 cm²

=> Area of 2nd circle = 1386 cm²

Now, we have to find radius.

$\sf{\implies Area\;of\;circle=1386\;cm^{2}}$

$\sf{\implies \pi r^{2}=1386}$

$\sf{\implies \dfrac{22}{7}\times r^{2}=1386}$

$\sf{\implies r^{2}=1386\times \dfrac{7}{22}}$

$\sf{\implies r^{2}=\dfrac{9702}{22}}$

$\sf{\implies r^{2}=441}$

$\sf{\implies r=21\;cm}$

=> Radius of circle = 21 cm.

Now, we will find the circumference of circle.

$\sf{\implies Circumference\;of\;circle=2\pi r}$

$\sf{\implies 2\times \dfrac{22}{7}\times 21}$

$\sf{\implies 2\times 22\times 3}$

$\sf{\implies 132\;cm}$

Hence, the circumference of a circle is 132 cm.