Question

In the figure above, the four circles have the same center and their radii are $1,2,3$ and $4$, respectively. What is the ratio of the area of the small shaded ring to the area of the large shaded ring?

• A. $1:2$
• B. $1:4$
• C. $3:5$
• D. $3:7$

Answer 1

The correct option is D $3:7$

We know that area of circle is $\pi \times r^2$, where $r$ is radius.

Area of small shaded ring is $\pi \times (2^2-1^2)=\pi \times 3$.

Area of large shaded region is $\pi \times (4^2-3^2)=\pi \times 7$.

The ratio of smaller to larger shaded regions is $\pi \times \frac{3}{\pi }\times 7=\frac{3}{7}$.