Question

A solid sphere r=3.5cmmelt and recast into a wire of d=7mm find the length of the wire

Answer 1

Step-by-step explanation:

radius of sphere = 3.5 cm

volume of sphere = 4/3 π r^3

$volume \: of \: sphere = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times \frac{22}{7} \times 3.5 \times 3.5 \times 3.5 \\ = \frac{4}{3} \times \frac{22}{2} \times 3.5 \times 3.5 \\ = \frac{4}{3} \times 11 \times 3.5 \times 3.5 \\ = \frac{4}{3} \times 11 \times 12.25 \\ = \frac{44 \times 12.25}{3} \\ = \frac{539}{3} \\ = 179.6$

diameter of wire = 7mm = 0.7 cm

radius = 0.7/2 = 0.35 cm

the wire is in cylindrical shape

volume of cylinder = πr^2h

$179.6= \frac{22}{7} \times 0.35 \times 0.35 \times h \\ h = \frac{179.6 \times 7}{22 \times 0.35 \times 0.35} \\ h = \frac{179.6 \times 20}{22 \times 0.35} \\ h = \frac{179.6 \times 10}{11 \times 0.35} \\ h = \frac{16.32 \times 10}{0.35} \\ h = 46.6 \times 10 \\ h = 466$

length of wire is 466 cm

hope you get your answer