Question

In the given figure the diameter of the biggest semicircle is 56 cm and the radius of the smallest circle is 7 cm. The area of the shaded portion is:

• A. $482c{m}^2$
• B. $462c{m}^2$
• C. $654c{m}^2$
• D. $804c{m}^2$

Answer 1

Answer: (B)

$462c{m}^2$

From the given diagram, we can see that,

Area of the shaded of portion $=$ Area of the large semicircle $-2\times$ Area of the the smaller semicircle $-$ Area of the smallest circle

Given that, the diameter of the large semicircle is $56cm$.

So, radius of the large semicircle $=\frac{56}{2}=28cm$

Since there are two semicircles along the diameter of the largest semicircle, radius of each semicircle $=\frac{28}{2}=14cm$

We know that area of a circle $=\pi r^2$
$\therefore$Area of the large semicircle $=\frac{1}{2}\times \pi (28{)}^2=\frac{1}{2}\times \frac{22}{7}\times 28\times 28$ [using $\pi =\frac{22}{7}$]

$\therefore$ Area of the large semicircle $=1232c{m}^2$

Also, area of the two smaller semicircles $=2\times \frac{1}{2}\pi (14{)}^2=\frac{22}{7}\times 14\times 14$

$\therefore$ Area of 2 small semicircles $=616c{m}^2$

And finally, area of the smallest circle $=\pi (7{)}^2=\frac{22}{7}\times 7\times 7$

$\therefore$ area of the smallest circle $=154c{m}^2$

Hence, area of the shaded region $=1232-(154+616)=462{cm}^2$

So, option B is correct.