A fresh water marine biologist needs to put an observation window in a tank. She

Question

A fresh water marine biologist needs to put an observation window in a tank. She has narrowed it down to the following two designs. The top of each window will be 20 feet below the surface of the water. The first is an isosceles triangle with a base of 6 ft and a height of 6 ft. The second is a rectangle combined with a semicircle. the rectangle is 3 ft across and the semicircle has a radius of 3 ft. Both windows are rated to withstand 40000 lbs of force. Which window (if either) should she choose? Explain

Explanation / Answer

All we need is that the area of the window must be maximum
so that observations can be made easier.

The first is an isosceles triangle with a base of 6 ft and a height of 6 ft :
Area = 1/2 * base * height

Area = 1/2 * 6 * 6

Area= 1/2 * 36

Area = 18 square feet ---> for isosceles triangle

The second is a rectangle combined with a semicircle. the rectangle is 3 ft across and the semicircle has a radius of 3 ft.
Area is :
Area of rectangle + Area of semicircle

Semicircle has radius of 3 feet

So, length of rectangle is diameter of semicircle = 2*3 = 6

So, area of rectangle is : 6 * 3 = 18 square feet

Now, area of semicircle is :
A = 1/2 * pi * r^2
A = 1/2 * pi * 3^2
A = 9pi/2

Total area is : 18 + 9pi/2
which is approx 32.1371669411540696

And this area is clearly larger than the area of the isosceles triangle

So, the biologist must choose :
The second window ----> ANSWER

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