Question

The radius of the sphere is 21 cm. It is melted and drawn into a wire of radius 7 cm. Find the length of the wire.

Answer 1

Given :

• Radius of sphere = 21cm
• It is melted to form a wire of radius 7cm

To find :

Length of wire

Formula used :

1. Volume of cylinder = πr²l
2. Volume of sphere = (4/3)πR³

Here,

• r = radius of cylinder
• l = length of cylinder
• R = radius of sphere

Solution :

Concept used - When one shape is melted to form new shape, volume remain constant, that is volume of original shape = Volume of new shape

Therefore , here volume of sphere = Volume of wire (cylinder)

$\sf \: \dfrac{4}{3} \pi \: R^3 \: = \pi \: {r}^{2} \: l \\ \\ \sf \implies \: \dfrac{4}{3} \times \pi \times ( {21cm)}^{3 } \: = \: \pi( {7cm)}^{2} \times l \\ \\ \sf \implies \: l \: = \: \dfrac{4}{3} \times \dfrac{\pi}{\pi} \times \dfrac{21 \times 21 \times 21}{7 \times 7} \: \dfrac{ {cm}^{3} }{ {cm}^{2} } \\ \\ \sf \implies \: l \: \: = \frac{4}{3} \times 1 \times(3 \times 3 \times 21) \: cm \: \\ \\ \sf \implies \: l \: = \: 4 \times 3 \times 21 \: cm \\ \\ \sf \implies \: l \: = \: 252cm$

ANSWER :

length of wire = 252cm = 2.52m