Question

Two concentric circles form a ring. If the inner and outer circumferences of the ring are 10$\pi$ cm and 30$\pi$ cm respectively, then the width of the ring is ___.

• A. 10 cm
• B. 20 cm
• C. 30 cm
• D. 40 cm

Answer 1

The correct option is A 10 cm

We know that the circumference of a circle of radius $r$ units is given by $2\pi r$ units.
Inner circumference of the ring = $10\pi$ cm
$\Rightarrow$ Radius of the inner circle in the ring = $\frac{10\pi }{2\pi }\text{cm}=5\text{cm}$
Outer circumference of the ring = $30\pi$ cm
$\Rightarrow$ Radius of the outer circle in the ring = $\frac{30\pi }{2\pi }\text{cm}=15\text{cm}$
Now, width of the circular ring equals the difference in the outer and inner radii.
$\therefore$ Width of the circular ring = $15\text{cm}-5\text{cm}=10\text{cm}$