Find diameter, circumference, and area of a circle if radius is $75\mathrm{cm}$.

Given:$r=75\mathrm{cm}$

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.

$$\begin{array}{lrcl}\because & d& =& 2r\\ \therefore & d& =& 2\times 75\\ \therefore & d& =& 150\mathrm{cm}\end{array}$$Therefore, the diameter of the given circle is $150\mathrm{cm}$.

Now, let's find circumference of the circle.

$$\begin{array}{lrcl}\because & C& =& 2\pi r\\ \therefore & C& =& 2\times 3.14\times 75\\ \therefore & C& =& 3.14\times 150\\ \therefore & C& =& 471\mathrm{cm}\end{array}$$Therefore, the circumference of the given circle is $471\mathrm{cm}$.

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

$$\begin{array}{lrcl}\because & A& =& \pi r^2\\ \therefore & A& =& 3.14\times {75}^2\\ \therefore & A& =& 3.14\times 5625\\ \therefore & A& =& 17662.5{\mathrm{cm}}^2\end{array}$$Therefore, the area of the given circle is $17662.5{\mathrm{cm}}^2$.