Question

The area of the shaded region between the circumferences of two concentric circles is 346.5 cm². The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle. [Take $\pi =\frac{22}{7}$]

• A. 35 cm
• B. 32 cm
• C. 17.5 cm

Answer 1

The correct option is C 17.5 cm

Let the radii of inner circle and outer circle be r and R respectively.
Then, $2\times \frac{22}{7}\times r=88$
$\therefore$ r = 14 cm.

Area of the inner circle
= $\frac{22}{7}\times 14\times 14c{m}^2=616c{m}^2$

Area of the outer circle
= (616 + 346.5) $c{m}^2$ = 962.5 $c{m}^2$

Then, $\frac{22}{7}\times R^2=962.5$
$⟹R^2=962.5\times \frac{7}{22}=6.25\times 7\times 7$
$⟹R=2.5\times 7$ = 17.5 cm