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Ten identical lengths of wire are laid closely

side-by-side. Their combined width is measured

and found to be 14.2 mm. Calculate:

a the radius of a single wire

b the volume in mm of a single wire if its

length is 10.0 cm (volume of a cylinder =

Tr’h, where r=radius and h= height).


Can you find b

Respuesta :

Edufirst

Answer:

  • a) The radius of a single wire is 0.710 mm

  • b) The volume of a single wire is 158 mm³

Explanation:

a) Calculate the radius of a single wire

Since ten identical lengths of wire are laid closely, the combined width is equal to the sum of the diameters of the ten wires.

That is:

  • [tex]Combined-width=10\times diameter[/tex]

From which you can solve for the diameter of a single wire:

[tex]14.2mm=10\times diameter\\ \\ \\ diameter=14.2mm/10=1.42mm[/tex]

The radius is half the diameter, so:

  • [tex]radius=1.42mm/2=0.710mm[/tex]

b) Calculate the volume in mm of a single wire if its length is 10.0 cm

The shape of one wire is cylindrical. So, the formula for the volume is:

  • [tex]Volume=\pi \times r^2\times L[/tex]

Where r is the radius and L is the length.

Since the width is given in mm, conver the length to mm too.

  • [tex]10.0cm\times 10mm/cm=100.mm[/tex]

And subsituting the values in the formula of the volume you get:

  • [tex]V=\pi \times (0.710mm)^2\times 100.mm=158.37mm^3[/tex]

That must  be rounded to 3 significant figures: 158 mm³.

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