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