Find the circumference of circle whose area is $16$ times the area of the circle with diameter $1.4\ cm$.

Academic Mathematics NCERT Class 10

Given: A circle whose area is $16$ times the area of the circle with diameter $1.4\ m$.

To do: To find the circumference of circle.

Solution:

Area of circle $4=16$ times of diameter

Diameter $=1.4\ m$

Now, Area of circle $=16\times 1.4$

$=22.4\ m^2$

Then, Area of circle$=\pi r^2$

$\Rightarrow \pi r^2=22.4$

$\Rightarrow r^2=\frac{22.4}{\pi}$

$\Rightarrow r^2=\frac{22.4}{\frac{22}{7}}$

$\Rightarrow r^2=\frac{22.4\times 7}{22}$

$\Rightarrow r^2=7.12$

$\Rightarrow r=\sqrt{7.12}$

$\Rightarrow r=2.67\ m$

Now, Circumference of circle $=2\pi r$

$=2\times \frac{22}{7}\times 2.67$

$=2\times 3.14\times 2.67$

$=16.76\ m$.

Thus, the circumference of the circle is $16.76\ m$.

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Updated on: 10-Oct-2022

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