Calculus

Application of Derivatives

Medium

An architect designs a garden in a circular shape with centre E and radius 50 m. There is a flower bed ABCD of rectangular shape inside the garden as shown in the figure. Suppose length and width of the flower bed are $2x$ and $2y$ meters respectively. Figure for CUET Mathematics 2022 17 Aug Shift 2 question 44 (Calculus)

Based on above information answer the following question :

The maximum area (in $m^2$ ) of the flower bed is :

1250

2500

5000

625

✅ Correct Option: 3

$A'(x) = 0$ gives $x^2 = 1250$ , so $x = \sqrt{1250}$ . Then $y^2 = 2500-1250 = 1250$ , so $y = \sqrt{1250}$ . Max area $= 4xy = 4\cdot 1250 = 5000$ $m^2$ .

Question 41

Based on above information answer the following question :

$x$ and $y$ will satisfy :

Question 42

Based on above information answer the following question :

The area of the flower bed $(A(x))$ is given by :

Question 43

Based on above information answer the following question :

$\frac{dA(x)}{dx} =$

Question 45

Based on above information answer the following question :

If area of the flower bed is maximum, then area (in $m^2$ ) of the garden, which is outside the flower bed is :

Based on above information answer the following question : The maximum area (in m2m^2m2) of the flower bed is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Based on above information answer the following question :

The maximum area (in $m^2$ ) of the flower bed is :