Question

Draw a graph for the radius and circumference of the circle using a suitable scale. (Hint: Take radius = 7, 14, 21 units, and so on) From the graph, (a) Find the circumference of the circle when the radius is 42 units. (b) At what radius will the circumference of the circle be 220 units?

Answer 1

Step 1: Let $x$ represents the radius of the circle and $y$represents the circumference of the circle.

Know that, $\mathrm{Circumference}=\mathit{2}\pi \times \mathrm{Radius}$

Therefore,

$y=2\pi x$

Step 2: Find the values of $y$ at $x=7,14,21,42$,

When$x=7$, then,

$\begin{array}{rcl}y& =& 2\times \frac{22}{7}\times 7\\ & =& 44\end{array}$

When $x=14$, then-

$\begin{array}{rcl}y& =& 2\times \frac{22}{7}\times 14\\ & =& 88\end{array}$

When $x=21$, then-

$\begin{array}{rcl}y& =& 2\times \frac{22}{7}\times 21\\ & =& 132\end{array}$

When $x=42$, then-

$\begin{array}{rcl}y& =& 2\times \frac{22}{7}\times 42\\ & =& 264\end{array}$

Draw the table:

$x$	$7$	$14$	$21$	$42$
$y$	$44$	$88$	$132$	$264$

Step 2: Draw the graph.

Step 3 : Find the radius $\text{'}x\text{'}$when circumference $y=220$.

$\begin{array}{l}220=2\times \frac{22}{7}\times x\\ \Rightarrow x=\frac{220\times 7}{2\times 22}\\ \Rightarrow x=35\end{array}$

Hence,

(a) The circumference of the circle when the radius is 42 units is $264$ radius.

(b) The circumference of the circle will be 220 units at $35$ unit radius