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In Fig.5. PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region. [Use $\pi = 3.14$]
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Given: In Fig.5. PSR, RTQ and PAQ are three semicircles of diameters $10\ cm$, $3\ cm$ and $7\ cm$ respectively.

To do: To find the perimeter of the shaded region.

Solution:

Radius of Semicircle PSR= $\frac{1}{2}$ x 10 =5 cm 

Radius of Semicircle RTQ =$\frac{1}{2}$x 3 = 1.5 cm

Radius of semicircle PAQ =$\frac{1}{2}$x 7 = 3.5 cm \ 

Circumference of the semi-circle PSR=$\pi \times 5=5\pi \ cm$

Circumference of the semi-circle RTQ=$\pi \times 1.5=1.5\pi \ cm$

Circumference of the semi-circle PAQ =$\pi \times 3.5=3.5\pi \ cm$

Perimeter of the shaded region = Circumference of semicircle PSR+ Circumference of semicircle RTQ+ Circumference of semicircle PAQ 

=$5\pi \ cm$+$1.5\pi \ cm$+$3.5\pi \ cm$

=10$\pi $

=10$\times $3.14

=31.4 cm

Therefore, perimeter of the shaded region is $31.4\ cm$.

 

Updated on: 10-Oct-2022

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