Question

A sphare diameter 30 cm is drawn into a wire 4 mm . What is the length of the wire that is creadted from the sphere ?

Answer 1

Solution :-

Given :
A sphere diameter 30 cm is drawn into a wire of diameter 4 mm.

We know that,
1 mm = 0.1 cm
By unitary method,
4 mm = 0.1 × 4 = 0.4 cm

Radius of sphere = R = 30/2 = 15 cm
Radius of wire = r = 0.4/2 = 0.2 cm

Let the length of the wire be h

According to the question,

Volume of sphere = Volume of wire/cylinder
=> 4/3 πR³ = πr²h
=> 4/3 × 22/7 × (15)³ = 22/7 × (0.2)² × h
=> 4/3 × 3375 = 0.04h
=> 13500/3 = 0.04h
=> 4500/0.04 = h = 112500


Hence,
Length of the wire = 112500 cm

Answer 2

▪️ Answer: 112500cm ▪️

▪️ Step by step solution:

Given,

The sphere diameter 30 cm is drawn into a wire of diameter 4 mm.

We will have to use unitary method.

➡️ 1 mm = 0.1 cm

➡️ 4 mm = 0.1 × 4 = 0.4 cm

➡️ 0.4 cm

⚫️ Radius of sphere =

$\frac{30}{2} = 15$

Volume of sphere = Volume of wire/cylinder

▪️ Let the length of the wire be X

=> 4/3 πR³ = πr²X

=> 4/3 × 22/7 × (15)³

=> 22/7 × (0.2)² × X

=> 4/3 × 3375

= 0.04x

=> 13500/3

= 0.04x

=> 4500/0.04

X = 112500

◼️ X = 112500 cm ◼️

Therefore,

Length of wire is 112500 cm