Question

A Solid ball of radius is 7cm was melted and then drawn into a wire of diameter 0.2cm . Find the length of wire

Answer 1

length of wires is 7 × 0.2 = answer

Answer 2

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

= 457.33 m

$\huge\underline\mathfrak{ExplanaTion:-}$

We have,

Radius of the lead ball = 7 cm

$\sf \: volume \: of \: th e\: lead \: ball = \frac{4}{3} \times \frac{22}{7} \times 7 \times 7 \times 7 \: {cm}^{3} \\ \\ \sf\: = \frac{4312}{3} \: {cm}^{3}$

Clearly, the wire is a cylinder of radius 0.1 cm.

★ Let the length of the wire be h cm. Then,

$\tt \: volume \: of \: wire = \frac{22}{7} \times 0.1 \times 0.1 \times h \\ \\ = \tt \frac{11h}{350}$

But, Volume of the wire = Volume of the lead ball

$\leadsto \sf \: \frac{11h}{350} = \frac{4312}{ 3} \\ \\ \leadsto \sf h = \frac{4312}{3} \times \frac{350}{11} \: cm \: \\ \\ \leadsto \sf \: \frac{4312 \times 350}{3 \times 11 \times 100} \: m \\ \\ \sf \: \rightarrow \: 457.33 \: m$