Question

A cube of metal with each edge 11 cm is melted to form a cylindrical wire of radius 1 mm. The length of the wire so obtained is (a) 421.75 m (b) 420.75 m (c) 423.50 m (d) 422.10 m​

Answer 1

Answer:

422.10m approx

Step-by-step explanation:

mark as brainlist answer please

Answer 2

Answer:

c) 423.5 m

$\rule{70mm}{2pt}$

Step-by-step explanation:

Given that a cube of metal with each edge 11 cm is melted to form a cylindrical wire of radius 1 mm. We need to find out the obtained length of the wire.

Assumption: Let's say that the length of the wire is x m.

$\underline{\underline{\green{\sf{As\:per\:given\: statement:}}}}$

“A cube of metal with each edge 11 cm.” (A cube is given with side 11 cm each.)

We know that-

$\huge{\underline{\boxed{\red{\sf{Vol.\:of\:cube\:=a^{3}}}}}}$

(where 'a' is side of cube and it's given value is 11 cm)

$\implies\:\sf{Vol.\:of\:cube\:=\:(11)^{3}}$

$\implies\:\sf{Vol.\:of\:cube\:=\:1331}$

$\underline{\underline{\green{\sf{As\:per\:given\: statement:}}}}$

“A cube of metal with each edge 11 cm is melted to form a cylindrical wire of radius 1 mm.” Therefore, the volume of cube is equal to volume of cylinder; as cube is melted to form a cylindrical wire.

We know that-

$\huge{\underline{\boxed{\red{\sf{Vol.\:of\:cylinder\:=\pi {r}^{2}h }}}}}$

Therefore,

$\gray{ \boxed{\sf{ \green{Vol.\:of\:cube\:=\:Vol.\:of\: cylinder}}}}$

Substitute the values,

$\implies\:\sf{1331=22/7\:\times\:r^{2}h}$

(Given value of radius is 1 mm. 1 mm = 0.1 cm and assumed value of length or height is x.)

$\implies\:\sf{1331=22/7\:\times\:(0.1)^{2}x}$

$\implies\:\sf{1331=22/7\:\times\:0.01x}$

$\implies\:\sf{\dfrac{1331(7)}{22(0.01)}=x}$

$\implies\:\sf{x=\dfrac{9317}{0.22}}$

$\implies\:\sf{x=42350cm}$

Now, to convert cm into m. Divide the value by 100. On solving we get,

$\implies\:\sf{\red{x=423.50m}}$

Therefore, the length of the wire is 423.5 m.