Question

The radius of the sphere is 7cm. It is melted and drawn into a wire of radius 0.3 cm. Find the length of the wire
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Answer 1

Step-by-step explanation:

radius of sphere = 7 cm

volume of sphere = 4/3 π r³

$= \frac{4}{3} \times \frac{22}{7} \times 7 \times 7 \times 7 \\ = \frac{4}{3} \times 22 \times 7 \times 7 \\ = \frac{88 \times 49}{3} \\ = \frac{4312}{3} \\ = 1437.33$

volume of sphere = 1437.33 cm³

this is equal to the volume of wire which is in cylindrical shape

volume of cylinder = πr²h

radius of cylinderical wire = 0.3 cm

$\pi {r}^{2} h = 1437.33 \\ \frac{22}{7} \times {(0.3)}^{2} \times h = 1437.33 \\ \frac{22}{7} \times 0.09 \times h = 1437.33 \\ h = \frac{1437.33 \times 7}{22 \times 0.09} \\ h = \frac{65.33 \times 7}{0.09} \\ h = 725.88 \times 7 \\ h = 5081.16 \: cm$

therefore the length of wire = 5081.16 cm

Hope you get your answer