a window is in the shape of a rectangle surmounted by a semicircle. if the width of the window is 3ft and the height of the window is 4ft, find the total area of the window 7th class question please give answer fastly
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Correct option is
C
2(π+4)k2 sq. unit
Perimeter of window when width is x and 2π is length.
→2x+2r+212πr=K⇒2x+r(2+π)=k
A=Area of window w=21πr2+2rx(area of rectangle + area of semicircle).
A=21πr2+r[k−r(2+π)]
A=r2[−2π,−2]+kr
For maximum area drdA=0 and dr2d2A<0
drdA=k−2r[2π]=0→[r=π+4k]
A=2π[
Perimeter of window when width is x and 2π is length.
→2x+2r+
2
1
2πr=K⇒2x+r(2+π)=k
A=Area of window w=
2
1
πr
2
+2rx(area of rectangle + area of semicircle).
A=
2
1
πr
2
+r[k−r(2+π)]
A=r
2
[−
2
π
,−2]+kr
For maximum area
dr
dA
=0 and
dr
2
d
2
A
<0
dr
dA
=k−2r[
2
π
]=0→[r=
π+4
k
]
A=
2
π
[
π+4
k
]
2
+2[
π+4
k
2
]→
2
(π+4
[
π+4
k
]
2
A=
2(π+4)
k
2
