The diagram shows an open tank for storing water, ABCDEF. The sides ABFE and CDEF are rectangles. The triangular ends ADE and BCF are isosceles, and ∠AED = ∠BFC = 90°. The ends ADE and BCF are vertical and EF is horizontal. Given that AD = x metres:

a. Show that the area of triangle ADE is 1/4 x² m² 

Given also that the capacity of the container is 4000 m³ and that the total area of the two triangular and two rectangular sides of the container is S m²:

b. Show that

Given that x can vary:

c. Use calculus to find the minimum value of S.

d. Justify that the value of S you have found is a minimum.

Transcribed Image Text:

S 2 + 16000/2 X