Q. 384.0( 15 Votes )

# In the given figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of shaded region.

Answer :

Given:

Diameter of semicircle PSR = 10 cm

⇒ Radius of semicircle PSR = = 5 cm = r_{1}

Diameter of semicircle RTQ = 3 cm

⇒ Radius of semicircle RTQ = = 1.5 cm = r_{2}

Diameter of semicircle PAQ = 7 cm

⇒ Radius of semicircle PAQ = = 3.5 cm = r_{3}

∵ Perimeter of semicircle = πr

∴ Perimeter of semicircle PSR = πr_{1}

= 3.14 × 5 = 15.7 cm

Similarly, Perimeter of semicircle RTQ = πr_{2}

= 3.14 × 1.5 = 4.71 cm

and Perimeter of semicircle PAQ = πr_{3}

= 3.14 × 3.5 = 10.99 cm

Perimeter of shaded region = Perimeter of semicircle PSR

+ Perimeter of semicircle RTQ

+ Perimeter of semicircle PAQ

= 15.7 + 4.71 + 10.99 = 31.4 cm

__Hence, the perimeter of the shaded region is 31.4 cm.__

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSIn the given figure, APB and CQD are semicircle of diameter 7 cm each, while ARC and BSD are semicircles of diameter 14 cm each. Find the (i) perimeter, (ii) area of the shaded region.NEXTIn the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle. IF OA = 20 cm, find the area of the shaded region. [Use π = 3.14]

Related Videos

RD Sharma | Area of Sector and Segment61 mins

RD Sharma | Area of Sector and Segments25 mins

Throwing the Light on Area of Sector43 mins

Champ Quiz | Area Related with the Circle45 mins

Surface Area and Volume49 mins

Surface Area and Volumes43 mins

Areas Related to Circle36 mins

RD Sharma | Imp Concepts : Surface Area And Volumes43 mins

RD Sharma | Imp. Qs. From Surface Area And Volumes47 mins

Quiz | Surface Area and Volumes42 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation