Calculus

Application of Derivatives

Easy

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 41 (Calculus)

Based on above information answer the following question :

$x$ and $y$ will satisfy :

$x^2 + y^2 = 50$

$x^2 + y^2 = 100$

$x^2 + y^2 = 2500$

$x + y = 50$

✅ Correct Option: 3

The diagonal of the rectangle equals the diameter $= 100$ . So $(2x)^2+(2y)^2 = 100^2$ , giving $x^2+y^2 = 2500$ .

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 :

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 : xxx and yyy will satisfy :

Solution

More from this set:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

Based on above information answer the following question :

$x$ and $y$ will satisfy :