Question

If the circumference of the two circles be $396$cm and $374$cm, find the area of the in-between region.

Answer 1

Since $396>374$

Outer circle has circumference $=396$cm and inner circle has circumference$=374$cm

Circumference of outer circle$=2\pi r=396$cm

$\Rightarrow 2\times \frac{22}{7}r=396$

$\therefore r=\frac{396}{2}\times \frac{7}{22}=63$cm

Area of outer circle$=\pi r^2=\frac{22}{7}\times 63\times 63=12,474{cm}^2$

Circumference of inner circle$=2\pi r=374$cm

$\Rightarrow 2\times \frac{22}{7}r=374$

$\therefore r=\frac{374}{2}\times \frac{7}{22}=59.5‬$cm

Area of inner circle$=\pi r^2=\frac{22}{7}\times 59.5\times 59.5=3,540.25‬{cm}^2$

$\therefore$ Area of the shaded region$=$Area of outer circle$-$Area of inner circle

$=12,474{cm}^2-3,540.25‬{cm}^2=8,933.75‬‬{cm}^2$