Question

39.
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.
Or​

Answer 1

Answer:

Thickness of wire = 0.033 cm

Step-by-step explanation:

Given :

Diameter of rod = 1 cm

Radius of rod = 1/2 = 0.5 cm

Height of rod = 8 cm

Find :

Thickness of wire.

$\bold{\underline{\underline{Solution\::}}}$

Volume of cylinder = πr²h

Substitute the known values in above formula

$\rightarrow{\sf{\frac{22}{7}\:\times\:(0.5)^2\:\times\:8}}$

$\rightarrow{\sf{\frac{22}{7}\:\times\:2}}$

$\rightarrow{\sf{\frac{44}{7}}}$ cm³ ___ (eq 1)

Now, copper rod is drawn into wire.

Volume remains conserved (same), whenever we change shapes.

$\bold{\underline{\underline{Assume:}}}$

Let the -

• thickness of wire be "r"

Height of rod = 18 m = 1800 cm

Volume of cylinder = πr²h

Substitute the known values in above formula

$\rightarrow{\sf{\frac{22}{7}\:\times\:r^2\:\times\:1800}}$ cm³ ___ (eq 2)

Now, (eq 1) = (eq 2)

As, Volume is same.

$\rightarrow{\sf{\frac{44}{7}}}$ = $\sf{\frac{22}{7}\:\times\:r^2\:\times\:1800}$

On solving we get,

$\sf{r}^2\:=\:\frac{1}{900}$

$\sf{r\:=\:\frac{\pm\:1}{30}}$

$\sf{r\:=\:\frac{1}{30}}$

$\sf{r\:=\:0.033}$ cm

∴ Thickness of the wire is 0.033 cm

Answer 2

$\huge{\mathfrak{\red{\underline{Answer :-}}}}$

0.033 cm

Solution :-

Case 1 :-

We know that,

$\Large{\boxed{\bf{Volume \: of \:cylinder\: = πr^{2}h}}}$

__________[Put Values]

(Putting π as 22/7)

→ 22/7 * (0.5)² * 8

→ (22 * 2)/7

→ 44/7

★ 44/7 cm³ ____[1]

Case 2 :-

Copper rod is drawn into wire.

Volume will be same

Assuming :-

Thickness of wire be "x"

Height of rod = 18 m = 1800 cm

$\Large{\boxed{\bf{Volume \: of \:cylinder\: = πr^{2}h}}}$

________[Put Values]

22/7 * r² * 1800 cm³ ___ (eq 2)

Now, (eq 1) = (eq 2)

As, Volume is same.

→44/7 = 22/7 * r² * 1800

→ r² = 1/900

→ r = ±1/30

→r = 0.033 cm

Hence, Thickness of the wire is 0.033 cm

$\large{\blue{\boxed{\underline{\mathcal{Radius \: of \:cylinder = 0.033 cm}}}}}$