Find diameter, circumference, and area of a circle if radius is $85\mathrm{cm}$.

Given:$r=85\mathrm{cm}$

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.

$$\begin{array}{lrcl}\because & d& =& 2r\\ \therefore & d& =& 2\times 85\\ \therefore & d& =& 170\mathrm{cm}\end{array}$$Therefore, the diameter of the given circle is $170\mathrm{cm}$.

Now, let's find circumference of the circle.

$$\begin{array}{lrcl}\because & C& =& 2\pi r\\ \therefore & C& =& 2\times 3.14\times 85\\ \therefore & C& =& 3.14\times 170\\ \therefore & C& =& 533.8\mathrm{cm}\end{array}$$Therefore, the circumference of the given circle is $533.8\mathrm{cm}$.

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

$$\begin{array}{lrcl}\because & A& =& \pi r^2\\ \therefore & A& =& 3.14\times {85}^2\\ \therefore & A& =& 3.14\times 7225\\ \therefore & A& =& 22686.5{\mathrm{cm}}^2\end{array}$$Therefore, the area of the given circle is $22686.5{\mathrm{cm}}^2$.