Question

The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. The
length of the wire in meters is
(a) 97.2
(b) 9,72
(c) 9720
(d) 972
ਇੱਕ ਗੋਲਾਕਾਰ ਦਾ ਅਰਧ-ਵਿਆਸ 9 cm ਹੈ । ਇਸ ਨੂੰ 2 mm ਵਿਆਸ ਦੀ ਇੱਕ ਤਾਰ ਦੇ ਰੂਪ ਵਿੱਚ
ਪਿਘਲਾਇਆ ਗਿਆ ਹੈ । ਮੀਟਰਾਂ ਵਿੱਚ ਤਾਰ ਦੀ ਲੰਬਾਈ ਹੈ
(a) 97.2
(b) 9.72
(c) 9720
(l 97​

Answer 1

To solve such problems, we need to remember some points

• Melting, recasting and transforming, if these words are in any question, then it means that we have to find the volume.

• Volume of sphere is equal to 4/3πr³

• Volume of cylinder is equal to πr²h

To find : Length of wire in meters

Given, The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm.

Calculate the volume of sphere

$\implies \sf \dfrac{4}{3} \pi r^3 \\ \\ \qquad{ \underline{ \pmb{ \sf{Put \: the \: value \: of \: radius}}}} \\ \\ \implies \sf \dfrac{4}{3} \times \dfrac{22}{7} \times (9)^3 \\ \\ \implies \sf \dfrac{4}{ \cancel 3} \times \pi \times { \cancel{9}} \: ^{3}\times 9 \times 9 \\ \\ \implies \sf 972\pi \: cm^3$

• Volume of a sphere is 972π cm³

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It is given in question that a sphere is melted and drawn into a wire of diameter 2 mm.

Convert "mm" into cm

• 1cm = 10mm

$\implies\sf 2 \times \dfrac{1}{10}$

$\therefore{\pmb{\sf{Diameter\:of\:the\:wire=0.2cm}}}$

If sphere is melted and drawn into a wire, then the volume of sphere is equal to volume of wire

⠀

$\bullet \: \tt Volume_{(sphere)} = Volume_{(wire)} \\ \\ { \underline{ \pmb{ \sf{Put \: the \: value \: of \: volume \: of \: sphere}}}} \\ \\ \implies \sf 972\pi = \pi r^2h \\ \\ { \underline{ \pmb{ \sf{Cancel \: \pi \: and \: put \: the \: value \: of \: radius \: of \: the \: wire}}}} \\ \\ \implies \sf 972 = \left(\dfrac{0.2}{2} \right)^2 \times h \\ \\ \implies \sf 972 = (0.1)^2 \times \: h \\ \\ \implies \sf h = \dfrac{972}{0.01}cm \\ \\ { \underline{ \pmb{ \sf{Convert \: cm \: into \: m \: and \: 1m = 100cm}}}} \\ \\ \implies \sf h = 972 \times { \cancel{100}} \times \dfrac{1}{ \cancel{100}} = 972m$

Final answer

• Length of the wire = 972m
• Correct option is (d)

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Answer 2

Volume of wire = Volume of sphere

=> πr²h = 4/3πr³

=> r²h = 4/3 r³ ×

=> (0.2/2)²×h = 4/3 × 729

=> (0.1)² × h = 4 × 243

=> 0.01 × h = 4 × 243

=> h = 4 × 243 × 100/100

=> 972 m