A window is in the shape of a rectangle surmounted by a semi-circle. I

1.	A window is in the shape of a rectangle surmounted by a semi-circle. If the perimeterof the window be 20 feet then find the maximum area.T1517 AP 17
Answer» Area of circle=πr2πr2 Area of rectangle=l×b=2×r×xl×b=2×r×x A=2rx+12πr2A=2rx+12πr2 =r[10−(π+2)r]+12πr2=r[10−(π+2)r]+12πr2 =10r−(12=10r−(12π+2)r2π+2)r2 For maximum areadAdrdAdr=0=0andd2Adr2d2Adr2is -ve. ⇒10−(π+4)r=0⇒10−(π+4)r=0 (π+4)r=10(π+4)r=10 r=10π+4

A window is in the shape of a rectangle surmounted by a semi-circle. If the perimeterof the window be 20 feet then find the maximum area.T1517 AP 17

Answer»

Area of circle=πr2πr2

Area of rectangle=l×b=2×r×xl×b=2×r×x

A=2rx+12πr2A=2rx+12πr2

=r[10−(π+2)r]+12πr2=r[10−(π+2)r]+12πr2

=10r−(12=10r−(12π+2)r2π+2)r2

For maximum areadAdrdAdr=0=0andd2Adr2d2Adr2is -ve.

⇒10−(π+4)r=0⇒10−(π+4)r=0

(π+4)r=10(π+4)r=10

r=10π+4