Question

In the following diagram there are four semi circular arcs and a shaded region. The diameter of largest semi circle is 28cm and of the smallest is 7cm. The area of shaded region is

• A. \(98.75 \pi\)
• B. \(120.5 \pi\)
• C. \(105.5 \pi\)
• D. \(110.25 \pi\)

Answer 1

The Correct Option is D

Step 1: Semicircle areas: the 28 cm diameter gives \(98\pi\), the 14 cm diameter gives \(24.5\pi\), and each 7 cm arc gives \(6.125\pi\).
Step 2: Combine as largest \(+\) middle \(-\) 2\(\times\)smallest: \(98\pi+24.5\pi-12.25\pi\).
Step 3: This gives \(110.25\pi\).
\[ \boxed{110.25\pi \text{ cm}^{2}} \]