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  • A wire of length 36 m cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is k (meter), then <img alt="\left ( \

A wire of length 36 m cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is k (meter), then \left ( \frac{4}{\pi } +1\right )k is equal to ________
 

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best_answer

Let x length be used for circle & 36-x for square

Area\: A= \pi \left ( \frac{x}{2\pi } \right )^{2}+\left ( \frac{36-x}{4} \right )^{2}
A= \frac{x^{2}}{4\pi }+\frac{\left ( 36-x \right )^{2}}{16}

\frac{dA}{dx}= 0
\Rightarrow \frac{2x}{4\pi }+\frac{2\left ( 36-x \right )\left ( -1 \right )}{16}= 0
\Rightarrow\, x= \frac{36\pi }{4+\pi }= circumference\; k
\therefore k\left ( \frac{4+\pi }{\pi } \right )= 36

Posted by

Kuldeep Maurya

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