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. 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 : Option 1: 1250( - 2) m^2 Option 2: 1250( + 2) m^2 Option 3: 2500( - 2) m^2 Option 4: 2500( + 2) m^2

Answer: 2500( - 2) m^2. Solution: Garden area = (50)^2 = 2500. Flower bed max area = 5000. Outside area = 2500 - 5000 = 2500(-2) m^2.

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 45 (Calculus)

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 :

$1250(\pi - 2)\,m^2$

$1250(\pi + 2)\,m^2$

$2500(\pi - 2)\,m^2$

$2500(\pi + 2)\,m^2$

✅ Correct Option: 3

Garden area $= \pi(50)^2 = 2500\pi$ . Flower bed max area $= 5000$ . Outside area $= 2500\pi - 5000 = 2500(\pi-2)$ $m^2$ .

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 44

Based on above information answer the following question :

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

Based on above information answer the following question : If area of the flower bed is maximum, then area (in m2m^2m2) of the garden, which is outside the flower bed is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

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 :