Question

The figure shows two circles with the same center. The radius of the larger circle is 10 cm, and the radius of the smaller circle is 4 cm. Find the shaded area between the two circles.

• A. $246c{m}^2$
• B. $264c{m}^2$
• C. $426c{m}^2$
• D. $462c{m}^2$
  

Answer 1

The correct option is D $462c{m}^2$


To find the area of the brown-shaded region, we have to subtract the area of the smaller circle from the area of the bigger circle.

Let radius of bigger circle = $R$
radius of smaller circle = $r$

Area of brown shaded region = $\pi \times (R^2-r^2)$

Substituting the values for $R$ and $r$,

Area of brown shaded region
$=\pi \times ({14}^2-7^2)=\pi \times (196-49)=(\frac{22}{7}\times 147)c{m}^2=(22\times 21)c{m}^2=462c{m}^2$