Q. 155.0( 3 Votes )

Answer :

Let the radius of semicircle, length and breadth of rectangle be r, x and y respectively

AE = r

AB = x = 2r (semicircle is mounted over rectangle) …1

AD = y

**Given:** Perimeter of window = 10 m

x + 2y + πr = 10

2r + 2y + πr = 10

2y = 10 – (π + 2).r

y = … 2

To admit maximum amount of light, area of window should be maximum

Assuming area of window as A

A = xy +

A = (2r) () +

A = 10r - πr^{2} – 2r^{2} +

A = 10r – 2r^{2} -

Condition for maxima and minima is

10 – 4r - πr = 0

= - 4 - π < 0

For r = A will be maximum.

Length of rectangular part = (from equation 1)

Breath of rectangular part = (from equation 2)

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PREVIOUSA tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m3. If building of tank cost Rs 70 per square metre for the base and Rs 45 per square matre for sides, what is the cost of least expensive tank?NEXTA large window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 metres find the dimensions of the rectangle that will produce the largest area of the window.

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