PQRS is a diameter of a circle of radius 6cm. The lengths PQ, QR and RS are equal. Semi circles are drawn on PQ and QS as diameters. Find the perimeter and area of the region so obtained.
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Solution:
PS=12cm
As PO=OR=RS
Therefore PO=OR=RS=1/3×PS=1/3×12=4cm
QS=2PO
OS=2×4=8cm
Area of shaded region=area of semicircle with PS as diameter+area of semicircle with PQ being the diameter-area of a semicircle with OS as a diameter.
=1/2{3.14×6²+3.14×2²-3.14×4²}
=1/2{3.14×36+3.14×4-3.14×16)
=1/2{3.14(36+4-16)}
=1/2(3.14×24)=1/2×75.35
Area of shaded region=37.68cm²
PS=12cm
As PO=OR=RS
Therefore PO=OR=RS=1/3×PS=1/3×12=4cm
QS=2PO
OS=2×4=8cm
Area of shaded region=area of semicircle with PS as diameter+area of semicircle with PQ being the diameter-area of a semicircle with OS as a diameter.
=1/2{3.14×6²+3.14×2²-3.14×4²}
=1/2{3.14×36+3.14×4-3.14×16)
=1/2{3.14(36+4-16)}
=1/2(3.14×24)=1/2×75.35
Area of shaded region=37.68cm²
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