Question

CBSE Class X

Maths - Surface Area And Volumes

A copper wire 4 mm in diameter is evenly wound about a cylinder whose length is 24 cm and diameter 20 cm do as to cover the whole surface. Find the length and weight of the wire assuming the specific density to be 8.88 gm/cm^3.

Answer 1

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Diameter of the wire = 4 mm = 0.4 cm

Length of the cylinder = 24 cm

Radius of the cylinder = 10 cm

No.of turns = Length of the cylinder / Diameter of the wire

= 24/0.4
= 60

length of one turn= Circumference of the base of the cylinder
= (2×3.14×10)cm
= 62.8cm
Length of 60 turns = (62.8×60)cm= 3768cm
Total length of the wire wrapped, l = 3768cm
Radius of the wire, r = (0.4/2)= 0.2 cm

Volume of the wire = πr^2l
= (3.14×0.2×0.2×3768)cm^3
=473.2608 cm^3 = 473.3cm^3

mass of the wire = volume × density
=( 473.3 ×8.88) gm
=4202.904 gm
= 4203 gm (approx.)

$hope \: it \: will \: help \: you....$

Answer 2

Here's the answer :)

Given :

Diameter of copper wire = 4 mm = 0.4 cm

Number of rounds required to cover 24 cm
$\sf{ = \frac{24}{0.4}}$

Diameter of cylinder = 20 cm

Now,

Length of wire in one round = circumference of cylinder

= π × d

= 20 × 3.14

= 62.8 cm

Now,

Length of wire in 60 rounds

= 60 × 62.8

= 3768 cm


Radius of wire =
$\sf{ \frac{0.4}{2} = 0.2} \: cm$

Volume of wire = π \times 0.2^2 \times 3768

= 473.2 cu. cm

Now,

Weight of wire = 473.2 × 8.88

= 4202.016

= 4202 grams { approx }

So,

Length of wire = 62.8 cm

Weight of wire = 4202 grams

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Thanks!!