SATHEE: Application of Derivatives 4 Question 12

Application of Derivatives 4 Question 12

####13. If $20 m$ of wire is available for fencing off a flower-bed in the form of a circular sector, then the maximum area (in sq. m) of the flower-bed is

(2017 Main)

(a) 12.5

(b) 10

(d) 30

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Answer:

Correct Answer: 13. (d)

Solution:

Total length $= 2 r + r θ = 20$

$\Rightarrow θ = \frac{20 - 2 r}{r}$

Now, area of flower-bed,

$\begin{aligned} A & = \frac{1}{2} r^{2} θ \\ \Rightarrow & A & = \frac{1}{2} r^{2} \frac{20 - 2 r}{r} \\ \Rightarrow & A & = 10 r - r^{2} \\ ∴ & \frac{d A}{d r} & = 10 - 2 r \end{aligned}$

For maxima or minima, put $\frac{d A}{d r} = 0$ .

$\begin{aligned} \Rightarrow 10 - 2 r & = 0 \Rightarrow r = 5 \\ ∴ A_{max} & = \frac{1}{2} (5)^{2} \frac{20 - 2 (5)}{5} \\ = \frac{1}{2} \times 25 \times 2 = 25 sq. m \end{aligned}$

Application of Derivatives 4 Question 12

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Application of Derivatives 4 Question 12

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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