Question

A solid copper sphere of radius 9 cm is melted and reformed into a wire of radius 1 mm. What will be the length of this wire? (Take π = 22/7)

A) 1166.4 metres B) 1458 metres C) 777.6 metres D) 972 metres

Answer 1

Given:-

• Radius (r) of solid copper sphere = 9cm = 90mm

• Radius of wire = 1mm

To find:-

• Length of wire?

Soluti0n:-

★ Volume of sphere = $\sf \dfrac{4}{3} \pi r^3$

$:\implies\sf \dfrac{4}{3} \times \pi \times 90 \times 90$

$:\implies\sf 972000 \pi mm^3$

Now,

★ Volume of wire( cylinder) = $\sf \pi r^2 h$

$:\implies\sf \pi \times 1 \times 1 \times l$

★ Volume of sphere = Volume of cylinder

$:\implies\sf 972000 \times \cancel{ \pi}= \cancel{ \pi} \times 1 \times 1 \times l$

$:\implies\sf l = 972000mm$

So, the length of wire is 972000mm or 972 metres or 97200 centimetres.

★ Hence, Option(D) is correct.

$\rule{200}3$