Question

The radius of a metallic sphere is 12cm.itcwas melted to make a wire of diameter 6mm .fund the length of the wire

Answer 1

Given :--

• Radius of Metallic Sphere = 12cm.
• Diameter of Wire = 6mm

To Find :---

• Length of wire = ?

Formula and concept used :---

→ when Any objected is melted to make any new object, their volume will be same .

→ Volume of Sphere = 4/3 * π * r³

→ Volume of Cylinder = π * r² * h

→ wire is in the shape of cylinder , whose length is Equal to the Height of cylinder . .

→ 1 cm = 10mm

→ 1m = 1000mm

→ 1km = 1000m

______________________________

Solution :---

Putting values we get,

→ Volume of Sphere = 4/3 * π * (120)³ ( as 12cm = 120mm)

Now, Radius of wire = 6/2 = 3mm .

Let, Length of wire is = H mm .

so,

→ Volume of Wire = π * (3)² * H

____________________________

Since,

Volume of Sphere = Volume of wire

→ 4/3 * π * (120)³ = π * (3)² * H

→ 4 * (120)³ = (3)³ * H

→ H = 4*(120)³/27

→ H = 256000 mm

______________________________

Now,

→ 1000mm = 1m

→ 256000mm = 256 m.

Hence, length of wire will be 256m .

Answer 2

❏QuesTion :-

→ Given above ↑

❏Answer :-

$\to \: \boxed { \sf h = 25600 \: cm \: or \: 256000 \: mm} \:$

❏To Find :-

→ Length of wire .

❏Used formulas :-

$\boxed{ \star} \boxed{ \sf volume \: of \: sphere = \frac{4}{3} \pi \: {r}^{2} } \\ \\ \boxed{ \star} \boxed{ \sf \: volume \: of \: cylinde = \pi {r}^{2} h }$

❏Solution :-

Given that ,

→ Radius of metallic sphere = 12 cm

→ Diameter of melted wire = 6 mm = 0.6 cm

• ° • After melt height of cylinder is equal to the length of melted wire .

Hence,

→ Volume of cylinder = Volume of sphere

$\to \sf diameter \: of \: wire \: = 0.6 \: cm \\ \sf \: hence \: \\ \to \sf radius \: of \: wire = \frac{0.6}{2} = 0.3 \: cm\\ \\ \bf \: hence \: \\ \\ \to \sf \: volume \: of \: cylinder \: = \pi \: {(0 .3)}^{2} \: h \\ \: \\ \bf and \: \\ \to \sf volume \: of \: sphere = \frac{4}{3} \pi \: {(12)}^{ 3} \: \\ \\ \star \sf volume \: of \: cylinder = volume \: of \: sphere \\ \\ \to \sf \pi \: \times {(0.3)}^{2} \times h \: = \frac{4}{3} \pi \: {(12)}^{3} \\ \\ \to \sf h = \frac{4 \times 12 \times 12 \times 12}{3 \times 0.3 \times 0.3 } \\ \\ \to \sf h = \frac{4 \times 4 \times 12 \times 12 \times 100}{3 \times 3} \\ \\ \to \sf h = 4 \times 4 \times 4 \times 4 \times 100 \\ \\ \to \sf \boxed { \sf h = 25600 \: cm \: or \: 256000 \: mm}$