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A wire of length 28 m …

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A wire of length 28 m is to be cut into 2pieces one of the pieces is to be made into a square and the other into a circle what should be the length of the two pieces so that the combined area of the square and the circle is minimal

Posted by Sneha Gupta 5 years, 8 months ago

CBSE > Class 12 > Mathematics

2 answers

Ritika Kumar 5 years, 8 months ago

Kyoki itna bara solution likhne me bahut dikkat hoti hai

Ritika Kumar 5 years, 8 months ago

Let the radius of circle be r and length of one side of square be a. Circumference of circle =2πr Circumference of square=4a According to question, 2πr+4a=28 ...(2) 4a^2=(28-2πr)^2/4 .... (1) For minimum area, dy/dr>0 πr^2 + 4a^2=dy/dr Putting the value of equation (1) πr^2 + (28-2πr)^2/4=dy/dr 2πr - 2.(28-2πr).2π/4=dy/dr 2πr-28π+2rπ^2 =dy/dr For area dy/dr=0 r-14+πr=0 r=14/(π+1) Since dy/dr>0, so it will give minimum area Putting the value of r in equation (2) We get a=7/(π+1) Length of wire used in making circle=28π/(π+1) Length of wire used in making square=28/(π+1) I hope this will help you Agar solution me dikkat ho to whatsapp pe contact kar lena

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