Question

The boundary of the shaded region in the adjoining figure is

A. 200 mm
B. 196 mm
C. 186 mm
D. 176 mm

Answer 1

Hint:
The given figure consists of three semicircles. We will first find the radius of the semicircles and then we will compute the circumference of the semicircle using the formula, as $\pi r$, where $r$ is the radius. Then, add circumference of all the semicircles to find the length of the total boundary.

Complete step by step solution:
Here, in the figure, there are three semicircles, where diameter of one semicircle is 56 cm and the diameter of the other two circles is 28 cm.

We will first calculate the circumference of all three circles.
Radius is half the diameter of the circle.
Hence, the radius of one semicircle with diameter as 56 cm as $\dfrac{{56}}{2} = 28cm$.
Also, the formula for the circumference of the semicircle is given as $\pi r$, where $r$ is the radius.
${P_1} = \left( {\dfrac{{22}}{7}} \right)\left( {28} \right) = 88mm$
Similarly, the radius of semicircle with diameter as 28 cm as $\dfrac{{28}}{2} = 14cm$.
${P_2} = \left( {\dfrac{{22}}{7}} \right)\left( {14} \right) = 44mm$
the boundary of third semicircle will also be 44mm
Hence, the boundary of the shaded region is \[88 + 44 + 44 = 176mm\]

Thus, option D is correct.

Note:
Circumference or perimeter gives the length of the boundary of that shape. Hence, we have calculated circumference of the semicircle. Also, when we find the circumference of the semicircle, it does not include the length of its diameter.