Question

A wire of circular cross section had a diameter of 2mm and a length of 350m. If the mass of the wire is 6.82kg, calculate it's density in g/cm³

Answer 1

Step-by-step explanation:

given

let D = 2mm = 0.2cm ( 1cm = 10mm)

Let R be the radius = D/2 = 0.2/2 = 0.1cm

L (length) = 350m = 35000cm ( 1m = 100cm)

m( mass) = 6.83kg = 6830g (1kg=1000g)

now density = mass /volume

We have to calculate volume of the wire and mass is already given.

let V be the volume of the wire

volume of cylinder = base area * length of cylinder

= πR^2 * L

= 3.14 * 0.1^2 * 35000

= 1,099cm^3

now density = 6830/1099

= 6.21 g/cm^3 (answer)

hope u understood it

Answer 2

Answer:

Density of the wire = 6.2g/cm³

Step-by-step explanation:

Given,

The diameter of the wire = 2mm

length of the wire = 350m

Mass of the wire = 6.82kg

To find

The density of the wire

Recall the formula

The volume of cylinder = πr²h, where 'r' is the radius and 'h' is the height of the cylinder

Density = $\frac{Mass }{volume}$

100cm = 1m

10mm = 1cm

1 kg = 1000g

Solution:

Since the cross-section of the wire is a circle, we can calculate the volume of the wire by the formula of the volume of the cylinder

Diameter = 2mm

Radius the wire = r = 1mm = $\frac{1}{10} cm$ = 0.1cm

Height = h =  length of the wire = 350m = 35000cm

Volume of the wire = $\frac{22}{7}$ ×(0.1)²× 35000

= 1100cm³

∴ The volume of the wire = 1100cm³

we have

Density of the wire = $\frac{Mass}{Volume}$

Mass = 6.82kg = 6.82*1000g = 6820g

Density of the wire = $\frac{6820}{1100}$ = 6.2g/cm³

Answer:

Density of the wire = 6.2g/cm³

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