Question

a piece of wire of length 246 cm is cut into 12 parts whose lengths are in an arithmetic progression. given that the sum of the lengths of the four shortest parts is 34 cm find the length of the longest part

Answer 1

Answer:

Given 4x+2πr=a

A=x

2

+πr

2

=

16

1

(a−2πr)

2

+πr

2

dr

dA

=0⇒r=

2(π+4)

a

dr

2

d

2

A

is +ve and hence minimum.

Now, 4x=a−2πr=a−

π+4

aπ

=

π+4

4a

⇒x=

π+4

a

⇒A=x

2

+r

2

π=

4(π+4)

a

2

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