Question

A school has decided to Give scholar's Batches to scholar students and they were designed As PQRS is the Diameter of the circle of radius 6cm and length PQ, PR, RS, are Equal. find the perimeter of the shaded portion and the area of non-shaded Portion. what is the importance of a Scholar's batches for students?

Answer 1

Dear Student


$$\begin{gathered} PS=12cm \\ AsPQ=QR=RS \\ therefore,PS=QR=RS=\frac{1}{3}\times 12=4cm \\ QS=2PQ \\ QS=2\times 4=8cm \\ therefore, \\ Areaofshadedregion=AreaofsemicirclewithPSasdiameter+AreaofsemicirclewithPQasdiameter-AreaofsemicirclewithQSasdiameter \\ =\frac{1}{2}\left[3.14\times 6^2+3.14\times 2^2-3.14\times 4^2\right] \\ =\frac{1}{2}\left[3.14\times 36+3.14\times 4-3.14\times 16\right] \\ =\frac{1}{2}\left[3.14\times \left(36+4-16\right)\right] \\ =\frac{1}{2}\left[3.14\times 24\right]=\frac{1}{2}\times 75.36 \\ areaofshadedportionis37.68c{m}^2 \\ Nowareaofnonshadedportion=areaofbiggercircle-areaofshadedportion \\ =3.14\times 6\times 6-37.68 \\ =113.04-37.68 \\ =75.36c{m}^2 \end{gathered}$$
$$\begin{gathered} perimeterofshadedportion=circumferenceofsemicircleformedbyPQRS+circumferenceofsemicircleformedbyPQ+circumferenceofsemicircleformedbyQS \\ =3.14\times 6+3.14\times 2+3.14\times 4 \\ =3.14\times \left(6+2+4\right) \\ =3.14\times 12 \\ =37.68cm \end{gathered}$$


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