Question

a sphere of diameter 6•0cm is moulded into a thin uniform wire of diameter 0•2mm.calculate the length of the wire in metres​

Answer 1

The length of the wire is 36 m.

Step-by-step explanation:

Given, Diameter of sphere = 6 cm

We know that, radius can be found by taking the half in the diameter value. So,

`\text { sphere radius, } R=(D)/(2)=(6)/(2)=3 \mathrm{cm}=3 * 10^(-2) \mathrm{m}`

Similarly,

`\text { wire radius, } r=(0.2)/(2)=0.1 \mathrm{mm}=1 * 10^(-3) \mathrm{m}`

We know the below formulas,

`\text {volume of sphere}=(4)/(3) * \pi * R^(3)`

`\text {volume of wire}=\pi * r^(2) * l`

When equating both the equations, we can find length of wire as below, where
`\pi=(22)/(7)`

`(4)/(3) * \pi * R^(3)=\pi * r^(2) * l`

`(4)/(3) * (22)/(7) *\left(3 * 10^(-2)\right)^(3)=(22)/(7) *\left(1 * 10^(-3)\right)^(2) * l`

The
`\pi` value gets cancelled as common on both sides, we get

`(4)/(3) * 27 * 10^(-6)=10^(-6) * l`

The
`10^(-6)` value gets cancelled as common on both sides, we get

`l=4 * 9=36 m`