Question

find the diameter of a circle and its circumference if its area is 25πcm²
please solve this in copy​

Answer 1

Answer:

Hence the diameter of the circle is 10 cm and its circumference is 31.4cm.

Step-by-step explanation:

As per the data provided in the given question.

The given data is as follows,

The area of a circle is $25\pi cm^{2} .$

We have to find the diameter of a circle and its circumference.

Here we will be using the formula of the area of a circle.

$A=\pi r^{2}$

Now we will substitute the value of A in the above formula.

$25\pi =\pi r^{2}$

Now we will shift the numerator $\pi$ of RHS to the denominator of LHS and the output sign will be positive.

$\frac{25\pi }{\pi } =r^{2}$

$\pi$ is cancel from the above equation.

[tex]25=r^{2} \\ r^{2} =25[/tex]

Now we will take the square root.

Further, we get

$r=\sqrt{25}$

The square root of 25 is 5.

$r=5\;cm$

Now we know that the diameter of a circle is 2 times of radius.

[tex]d=2\times r\\ d=2\times5\\ d=10\;cm[/tex]

Now we will find the circumference of a circle.

Here we will be using the formula of the circumference of a circle.

$Circumference=2\pi r$

Now we will substitute the value of r and $\pi$ in the above formula. The value $\pi$ of a is 3.14.

[tex]=2\times\ 3.14\times5\\ =6.28\times5\\ =31.4\;cm[/tex]

Hence the diameter of the circle is 10 cm and its circumference is 31.4cm.