Question

A solid gold ball of radius 7 cm was melted and then drawn into a wire of diameter 0.2

cm. Find the length of the wire.​

Answer 1

we have :-

• the radius of ball = 7 cm .
• the diameter of wire i.e diameter of cylinder = 0.2 cm radius = 0.1 cm

To find :-

• the length of the wire i.e height of cylinder .

Formula used :-

• volume of sphere = 4/3πr³
• volume of cylinder = πr²h

A.T.Q

$\bf \: \dfrac{4}{3} \pi {r}^{3} = \pi {r}^{2} h \\ \\ \\ \red\implies \bf \: \dfrac{4}{3} \cancel\pi {r}^{3} = \cancel \pi {r}^{2} h \\ \\ \blue\implies\bf \frac{4}{3} \times7 \times 7 \times 7 = 0.1 \times 0.1 \times h \\ \\ \\ \green\implies\bf \: h \: = \frac{4 \times 7 \times 7 \times 7}{3 \times 0.1 \times 0.1 } \\ \\ \\\pink\implies \bf h \: = \frac{1372}{0.003} \\ \\ \\ \fbox{ \bf \: h = 457333.33\: cm}$

so lenght of the wire = 457333.33 cm .

additional information :-

here, in such type of questions when any object melt to form another object then their areas will be different but volume will remains same .

Answer 2

Answer:

• Length of wire = 457.34 m  [approx.]

Explanation:

Given

• A solid gold ball has a radius, R = 7 cm
• This solid ball is melted and drawn into a wire
• Diameter of wire, d = 0.2 cm

To find

• Length of wire, h =?

Formula required

• Formula for volume of sphere with radius 'R'

        Volume of sphere = 4/3 π R³

• Formula for volume of cylinder with radius 'r' and height 'h'

       Volume of cylinder = π r² h

Solution

Given diameter of wire is, d = 0.2 cm

so, Radius of wire, r = 0.2/2 cm = 0.1 cm

Wire that is drawn on melting the spherical ball would be in cylindrical shape.

therefore,

→ Volume of cylindrical wire = Volume of spherical ball

→ π r² h = 4/3 π R³

[ dividing by π both sides we will get]

→ r² h = 4/3  R³

→ ( 0.1 )² h = 4/3  (7)³

→ 0.01  h = 4/3  × 343

→ h = ( 4 × 343 ) / ( 3 * 0.01 )

→ h = 1372 / 0.03

→ h = 45733.34  cm

→ h =  45733.34 / 100  m

→ h = 457.34 m  [approx.]

Therefore,

• Approximate length of wire would be 457.34 metres.