Question

The radius of the sphere is 7cm. It is melted and drawn into a wire of radius 0.3cm. Find the length of the wire.​

Answer 1

$Volume \: of \: sphere = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \pi {(7)}^{3} \\ = \frac{4}{3} \times 343 \times \pi \\ = 457.33\pi$

Volume of sphere and wire will be same. SO,

Length of wire = h

$volume \: of \: wire = \pi {r}^{2} h \\ 457.33\pi = \pi \times {(7)}^{2} \times h \\ 457.33\pi = 49\pi \: h \\ h = \frac{457.33\pi}{49\pi} \\ h = \frac{457.33}{49} \\ h = 9.33 \:c m \: (answer)$

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