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Mensuration: Areas and Volumes · Question 65 of 68

Question 65

MediumOriginal question

A copper ball of diameter 6 cm is melted and drawn into a wire of diameter 0.2 cm. How long is the wire?

3.6 mCorrect answerYour answer9 mCorrect answerYour answer27 mCorrect answerYour answer36 mCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Ball: radius 3 cm, volume $\frac{4}{3}\pi \times 27 = 36\pi$ cm³.
Wire: a long cylinder of radius 0.1 cm, volume $\pi \times 0.01 \times L$ .
$0.01L = 36$ , so $L = 3{,}600$ cm = 36 m.

Worth noting

9 m uses 0.2 cm as the wire's radius and 27 m forgets the $4/3$ . 3.6 m divides 3,600 cm by 1,000 instead of 100.

Concept: Sphere drawn into a wire
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsMelting, recasting and combined solids

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