Find diameter, circumference, and area of a circle if radius is $50\mathrm{cm}$.

Given:$r=50\mathrm{cm}$

To find: diameter, circumference, area of the circle

Solution:

First, let's find diameter.
We know that, diameter is twice the length of the radius.

$$\begin{array}{lrcl}\because & d& =& 2r\\ \therefore & d& =& 2\times 50\\ \therefore & d& =& 100\mathrm{cm}\end{array}$$Therefore, the diameter of the given circle is $100\mathrm{cm}$.

Now, let's find circumference of the circle.

$$\begin{array}{lrcl}\because & C& =& 2\pi r\\ \therefore & C& =& 2\times 3.14\times 50\\ \therefore & C& =& 3.14\times 100\\ \therefore & C& =& 314\mathrm{cm}\end{array}$$Therefore, the circumference of the given circle is $314\mathrm{cm}$.

Now, let's find the area of the circle.

$$\begin{array}{lrcl}\because & A& =& \pi r^2\\ \therefore & A& =& 3.14\times {50}^2\\ \therefore & A& =& 3.14\times 2500\\ \therefore & A& =& 7850{\mathrm{cm}}^2\end{array}$$Therefore, the area of the given circle is $7850{\mathrm{cm}}^2$.