Question

Take 2 metres long wire and cut 10% of the wire. Then cut 10% of the remaining wire.
Repeat this three times. Then measure the length of the wire.
Verify your length of the wire in each part using compound interest formula (Taking (-ve)
sign in the formula as this is depreciation method).

Answer 1

Answer:

Total length of wire=10m

Let 'a' be length of part cut and bent into circle

∴2πr=a

r=

2π

a

Let (10−a) be length of part bent into equilateral triangle

∴3S=(10−a)

S=(

3

10−a

)

Combined area of two figures=πr

2

+

4

3

S

2

A=π(

4π

2

a

2

)+

4

3

(

3

10−a

)

2

A=

4π

a

2

+

36

3

(a

2

−20a+100)

A=(

4π

1

+

36

3

)a

2

−

9

5

3

a+

9

25

3

A

′

=2(

4π

1

+

36

3

)a−

9

5

3

=0

⇒a=

2π

1

+

18

3

9

5

3

=

(

2π

9

+

2

3

)

5

3

∴a=

9+π

3

10π

3

,10−a=

9+π

3

90

Wire must be cut in ration, a:10−a=π:3

3