Question

If area of the ring is $\frac{352}{7}$ $c{m}^2$ and inner radius is 3 cm, then find the circumference of outer circle.

• A. $\frac{110}{7}$ cm
• B. $\frac{220}{7}$ cm
• C. $\frac{440}{7}$ cm
• D. $\frac{880}{7}$ cm

Answer 1

The correct option is C $\frac{440}{7}$ cm

Area of ring = $\pi$($R^2$ - $r^2$)
$\frac{352}{7}$ = $\frac{22}{7}$($R^2$ - $3^2$)
$\frac{352}{22}$ = $(R^2$ - 9)
16 = ($R^2$ - 9)
$R^2$ = 16+9 = 25
R = $\sqrt{2}5$ = 5 cm
Circumference = 2$\pi$R
= 2$\times$$\frac{22}{7}$$\times$5 = $\frac{440}{7}$ cm