Question

Two concentric circles form a ring. The inner and outer circumferences of the ring are $50\frac{2}{7}m$ and $75\frac{3}{7}m$ respectively. Find the width of the ring.

• A. $3m$
• B. $4m$
• C. $5m$
• D. $6m$

Answer 1

The correct option is B $4m$

Inner circumference of ring = $50\frac{2}{7}m$

Outer circumference of ring = $75\frac{3}{7}m$

To find:- Width of ring

Solution:-

Formula for circumference = $2\pi \times radius$

Let the outer and inner radius of ring be $R$ and $r$ respectively.

$\therefore \text{inner circumference of ring}=50\frac{2}{7}m$

$\Rightarrow 2\pi r=50\frac{2}{7}$

$\Rightarrow 2\times \frac{22}{7}\times r=50\frac{2}{7}$

$\Rightarrow 44r=352\Rightarrow r=8$

$\therefore \text{outer circumference of ring}=75\frac{3}{7}m$

$\Rightarrow 2\pi R=75\frac{3}{7}$

$\Rightarrow 2\times \frac{22}{7}\times R=75\frac{3}{7}$

$\Rightarrow 44R=528\Rightarrow R=12$

Hence,

Width of ring = Inner circumference of ring - Outer circumference of ring = $12-8=4m$

Hence the correct answer is $4m$.