Question

A copper rod of diameter 1 cm and length 8 cm is drawn in to a wire of
length 18 m of uniform thickness. Find the thickness of wire
​

Answer 1

$\Huge{\underline{\boxed{\bf{\orange{Answer\::}}}}}$

$\rightarrow$ = $\huge\frac{1}{15}$

• $\large{\underline{\underline{\bf{Given\::}}}}$

● A copper rod of diameter 1 cm and length 8 cm.

● It is drawn in to a wire of length 18 m of uniform thickness.

• $\large{\underline{\underline{\bf{To \:Find\::}}}}$

● The thickness of wire.

Solution :-

Volume of copper rod = Volume of wire.

Volume of copper rod :

Coppwr rod is in the form of cylinder with diameter of rod = 1cm

So, radius = r = $\frac{1}{2}cm$

And lenght = height = 8cm.

Volume of copper rod : π r2 h.

$\rightarrow$ = π × (1/2)2 × 8

$\rightarrow$ = π × 1/4 × 8

$\rightarrow$ = 2π cm3

Volume of wire :

Wire is in the form of cylinder with radius = r

As length is equal to height so,

Height = 18 m = 18 × 100 = 1800 cm.

Volume of wire : π r2 h.

$\rightarrow$ = π r2 × 1800 cm.

$\rightarrow$ = 1800πr2 cm2.

Now,

Volume of copper rod = Volume of wire.

$\rightarrow$ = 1800πr2 = 2π

$\rightarrow$ = 1800r2 = 2

$\rightarrow$ = r2 = $\frac{2}{1800}$

$\rightarrow$ = r2 = $\frac{1}{900}$

$\rightarrow$ = r = $\sqrt{\frac{1}{900}}$

$\rightarrow$ = r = $\sqrt{\frac{1}{30×30}}$

$\rightarrow$ = r = $\frac{1}{30}$

So radius is = $\frac{1}{30}$

Theirfore, thickness of wire = Diameter of wire.

$\rightarrow$ = 2r

$\rightarrow$ = 2 × $\frac{1}{30}$

$\rightarrow$ = $\frac{1}{15}$

Final answer = $\frac{1}{15}$

Answer 2

≡QUESTION≡

A copper rod of diameter 1 cm and length 8 cm is drawn in to a wire of

length 18 m of uniform thickness. Find the thickness of wire .

                                                                                     

║⊕ANSWER⊕║

​

GIVEN

Diameter of the copper rod = 1 cm

So, radius(r) of the copper rod = 1/2 cm

Let R is the radius of the cross section(circular) of the wire.

Now, according to the question,

πR² *(18*100) = π(1/2)2 *8

=> R² *(18*100) = (1/2)2 *8

=> R² *(18*100) = 8/4

=> R² *(18*100) = 2

=> R² = 2/(18*100)

=> R² = 1/(9*100)

=> R = √{1/(9*100)}  

=> R = 1/(3*10)

=> R = 1/30

Now, thickness of the wire = 2r

                                               = 2 * 1/30

                                               = 2/30

                                               = 1/15

                                                = 0.067 cm