Question

A sphere of radius 7.0cm is molded into a thin uniform wire of diameter 0.2m. Calculate the length of the wire in meters.

Answer 1

$\bf{\underline{Solution :-}}$

• Sphere of radius = 7.0cm
• Diameter = 0.2 , then radius = 0.1cm

Volume of sphere = 4/3πr³

So,

→ 4/3 × 22/7 × 7 × 7 × 7

→ 4/3 × 22 × 49

→ 4/3 × 1078

→ 1437.44 cm³

Now,

Volume of sphere = Volume of wire

→ 1437.44 = Volume of wire (πr²h)

→ 1437.44 = πr²h

→ 1437.44 = 22/7 × 0.1 × 0.1 × h

→ h = 1437.44 × 22 × 0.2 ÷ 7

→ h = 903.53cm

$\bf{\underline{Hence:-}}$

• Height = 903.53cm

Answer 2

Given :

• A sphere of radius 7.0 cm is molded into a thin uniform wire of diameter 0.2 m .

To find :

• The length of the wire in meters.

Solution :

• Radius of sphere = 7.0 cm = 0.07 m

Formula used :-

${\boxed{\sf{Volume\:of\:sphere=\dfrac{4}{3}\pi\:r^3}}}$

Therefore,

Volume of sphere ,

= $\sf{\dfrac{4}{3}\times\pi\:0.07\times\:0.07\times\:0.07\:m^3}$

• Diameter of wire = 0.2 m
• Radius of wire =0.2/2 = 0.1 m

Here the wire is a cylinder.

Formula used :-

${\boxed{\sf{Volume\:of\:cylinder=\pi\:r^2h}}}$

Volume of wire = $\sf{\pi\times\:0.1\times\:0.1\times\:h\:m^3}$

According to the question :-

Volume of sphere = Volume of wire

⇒4/3×π×0.07×0.07×0.07=π×0.1×0.1×h

⇒4×0.07×0.07×0.07=0.1×0.1×h×3

⇒h = 0.046

Therefore the length of the wire is 0.046 m.