Question

A copper wire of diameter 6 mm is evenly wrapped on the cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and volume of the wire.

Answer 1

Step-by-step explanation:

Weight of wire is 980.1 gm.

Step-by-step explanation:

Diameter of wire = 6 mm = 0.6 cm

Radius of wire = \frac{Diameter}{2}

2

Diameter

=\frac{0.6}{2}=0.3 cm

2

0.6

=0.3cm

Height of cylinder = 15 cm

Diameter of cylinder = 49 cm

Radius of cylinder = \frac{Diameter}{2}

2

Diameter

=\frac{49}{2}

2

49

No. of rotations of wire on cylinder = \frac{\text{Height of cylinder}}{\text{Diameter of wire}}

Diameter of wire

Height of cylinder

= \frac{15}{0.6}

0.6

15

= 2525

Circumference of cylinder =2 \pi r= 2 \times \frac{22}{7} \times \frac{49}{2}2πr=2×

7

22

×

2

49

=154cm154cm

So, length of wire = 154 \times 25=3850 cm154×25=3850cm

Volume of wire =\pi r^2 h= \frac{22}{7} \times 0.3^2 \times 3850 = 108.9 cm^3πr

2

h=

7

22

×0.3

2

×3850=108.9cm

3

Weight of wire = Volume \times Density = 108.9 \times 9 = 980.1 gmVolume×Density=108.9×9=980.1gm

Thus the weight of wire is 980.1 gm.