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Pqrs is a Diameter of a Circle of Radius 6 Cm. the Lengths Pq, Qr and Rs Are Equal. Semicircles Are Drawn with Pq and Qs as Diameters, as Shown in the Given Figure. If Ps = - Mathematics

Sum

PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semicircles are drawn with PQ and QS as diameters, as shown in the given figure. If PS = 12 cm, find the perimeter and area of the shaded region.

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Solution

Perimeter (circumference of the circle) = 2πr
We know:
Perimeter of a semicircular arc = πr
Now,
For the arc PTS, radius is 6 cm.
∴ Circumference of the semicircle PTS =πr = 6π cm

For the arc QES, radius is 4 cm.
​∴ Circumference of the semicircle QES = πr = 4π cm

For the arc PBQ, radius is 2 cm.
∴ Circumference of the semicircle PBQ = πr = 2π cm

Now,
Perimeter of the shaded region == 6π + 4π + 2π

= 12πcm

= 12 ×3.14

= 37.68 cm

Area of the semicircle PBQ `=1/2 pi"r"^2`

`= 1/2xx3..14xx2xx2`

= 6.28 cm

Area of the semicircle PTS `= 1/2pi"r"^2`

`=1/2xx3.14xx6xx6`

= 56.52 cm2

Area of the semicircles QES `= 1/2pi"r"^2`

`=1/2xx3.14xx4xx4`

= 25.12 cm

Area of the shaded region = Area of the semicircle PBQ + Area of the semicircle PTS - Area of the semicircle QES = 6.28 + 56.52 - 25.12 =  37.68 cm2
                                           

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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Exercise 18B | Q 59 | Page 836
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