Question

A copper sphere of diameter 12cm is drawn into a wire of diameter 8mm.find the length of the wire

Answer 1

$\huge\underline\frak\red{Given:-}$

• A copper sphere of diameter 12cm is drawn into a wire of diameter 8mm

$\huge\underline\frak\red{Find\:out}$

• Find the length of the wire

$\huge\underline\frak\red{Solution}$

• Radius of copper = 12/2 = 6cm
• Volume of copper sphere

$\implies\sf \frac{4}{3}πr^3$

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

$\implies\sf \frac{4×22×2×6×6}{7}$

$\implies\sf \cancel\frac{6336}{7}$

$\implies\sf 905.14cm^3$

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

★ 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

$\implies\sf 905.14=πr^2h$

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

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

$\implies\sf h=\frac{905.14×7}{3.52}$

$\implies\sf h=1799.99cm$

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

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

$\huge\underline\frak\red{note}$

• 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

Answer 2

$\huge\underline\mathrm\green{Question}$

A copper sphere of diameter 12cm is drawn into a wire of diameter 8mm.find the length of the wire

$\huge\underline\mathrm\green{Find\:out}$

find the length of the wire

$\huge\underline\mathrm\green{Solution}$

Radius of copper sphere = 12/2 = 6cm

Volume of copper sphere

$\implies\sf \frac{4}{3}πr^3$

$\implies\sf \frac{4}{3}π×(6)^3$

$\implies\sf \frac{864π}{3}$cm³

So, Volume of copper sphere is equal to the volume of new wire

Diameter of wire = 8mm

Radius of wire = 8/2 = 0.4cm

$\implies\sf \frac{864π}{3}=πr^2h$

$\implies\sf \frac{864}{3}=(0.4)^2h$

$\implies\sf \frac{864}{3}=0.16h$

$\implies\sf h=\frac{864}{3×0.16}=1800cm=18m$

Note :-

• Volume of cylinder = πr²h
• Volume of sphere = 4/3πr³
• curved surface area of cylinder = 2πrh
• 100m = 1m
• 1km = 1000m