Math, asked by jehom, 3 months ago

. A copper sphere of diameter 12cm is melted and drawn into a wire of diameter 2mm. Find the length of the

wire.​

Answers

Answered by madhurimula1992
0

Answer:

Radius of copper = 12/2 = 6cm

Volume of copper sphere

\implies\sf \frac{4}{3}πr^3⟹

3

4

πr

3

\implies\sf \frac{4}{3}×\frac{22}{7}×6×6×6⟹

3

4

×

7

22

×6×6×6

\implies\sf \frac{4×22×2×6×6}{7}⟹

7

4×22×2×6×6

\implies\sf \cancel\frac{6336}{7}⟹

7

6336

\implies\sf 905.14cm^3⟹905.14cm

3

\large{\boxed{\bf{Volume\:of\:sphere=905.14cm^3}}}

Volumeofsphere=905.14cm

3

★ The volume of the new wire will be the same as the volume of the earlier copper sphere

Hence,

★ To find the length of wire we apply volume formula of cylinder i.e wire is also just like cylinder and take height as a length of cylinder

Radius of wire = 8/2=4mm=4/10=0.4cm

Volume of copper = Volume of wire

sphere

\implies\sf 905.14=πr^2h⟹905.14=πr

2

h

\implies\sf 905.14=\frac{22}{7}×0.4×0.4×h⟹905.14=

7

22

×0.4×0.4×h

\implies\sf 905.14=\frac{3.52h}{7}⟹905.14=

7

3.52h

\implies\sf h=\frac{905.14×7}{3.52}⟹h=

3.52

905.14×7

\implies\sf h=1799.99cm⟹h=1799.99cm

\implies\sf h=\frac{1799.99}{100}=17.9m\:approx⟹h=

100

1799.99

=17.9mapprox

\large{\boxed{\bf{length\:of\:wire=17.9m}}}

lengthofwire=17.9m

\huge\underline\frak\red{note}

note

Volume of Cylinder = πr²h

Volume of sphere = 4/3πr³

Volume of cone = 1/3πr³h

Volume of cuboid = l×b×h

Volume of cube = a³→where a is side

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