The diagram shows a window made from a rectangle with base 2r m and height h m and a semicircle of radius r m The perimeter of the window is 6 m and the surface area is A m 2 a Express h in terms of r b Show that A 6r 2r 2 r 2 c Find dA dr and d 2 A dr 2 d Find the value for r for which there is a stationary value of A e Determine the magnitude and nature of this stationary value rm hm 2rm

Question: The diagram shows a window made from a rectangle with base 2r m and height h m and a semicircle of radius r m. The

The diagram shows a window made from a rectangle with base 2r m and height h m and a semicircle of radius r m. The perimeter of the window is 6 m and the surface area is A m².

a. Express h in terms of r.

b. Show that A = 6r – 2r² – ½ πr².

c. Find dA/dr and d²A/dr².

d. Find the value for r for which there is a stationary value of A.

e. Determine the magnitude and nature of this stationary value.

rm hm 2rm

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