# Case study Chapter 6 (Application of Derivative)

Case study 2:- Read the following and answer the question.(Case study application of derivative 2)

Dr. Ritam residing to Delhi went to see an apartment of 3 BHK in Noida. The window of the house was in the form of a rectangle surmounted by a semicircular opening having a perimeter of the window 10 m as shown in figure.

(i) If x and y represents the length and breadth of the recangular region, then the relation between the variable is

(a)                (b)

(c)          (d) 2x + 2y = 10

(ii) The area of the window (A) expressed as a function of x is

(a)          (b)

(c)              (d)

(iii) Dr. Ritam is interested in maximising the area of the whole window. For this to happen the value of x should be

(a) 20/π                         (b) 20/(4-π)

(c) 20/(2+π)                  (d) 20/(4+π)

(iv) For maximum value of A, the breadth of rectangular part of window is

(a) 20/(4+π)                 (b) 20/π

(c) 10/(4+π)                   (d) 5/(2+π)

(v) The maximum area of window is

(a) sq.m              (b) sq.m

(c) sq.m         (d) sq.m

Since perimeter of window = x + y + y + perimeter of semicircle

[Since radius of semicircle is x/2]

Since,

For maximum value of A

Since,

Area of window = ar(rectangular part) + ar( semi circular part)

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## Some other Case study problem

Case study 1: Read the following and answer the question(Case study application of derivative 1 )
A recangular hall is to be developed for a meeting of farmers in an agriculture college to aware them for new technique in cultivation. It is given that the floor has a fixed perimeter P as shown below.

Case study 3:- Read the following and answer the question:(Case study application of derivative 3)

On the request of villagers, a construction agency designs a tank with the help of an architect. Tank consist of rectangular base with recangular sides, open at the top so that its depth is 2 m and volume is 8 cubic meter as shown below:

Case study 4:- Read the following and answer the question:(Case study application of derivative 4 )

These days chinese and Indian troops are engaged in aggressive melee,face-off skirmishes at location near the disputed Pangong Lake in Ladakh.

One day a helicopterof enemy is flying along the curve represented by y = x² + 7. A soldier placed at (3, 7) wants to shoot down the helicopter when it is nearest to him.