Question

Exercise - 10.4
1) A metallic sphere of radius 4a cm is melted and recast
into the shape of a cylinder of radius of 6cm. find
the height of the cylinder.​

Answer 1

Correct Question :-

• A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Given :-

• Radius of metallic sphere (R) = 4.2 cm.
• Radius of cylinder (r) = 6 cm.

To Find :-

• Height of the cylinder (h).

Solution :-

We know,

• Formula for finding volume of sphere = $\rm{\dfrac{4}{3}{\pi}R^3}$

Then,

Volume of given metallic sphere =

$\implies\rm{\dfrac{4}{3}{\pi}\times{}(4.2)^3}$

$\implies\rm{\dfrac{4\times{}4.2\times{}4.2\times{}4.2}{3}{\pi}\:cm^3}$

Now,

• Formula for finding volume of a cylinder = $\rm{{\pi}r^2h}$

Then,

Volume of the given cylinder =

$\implies\rm{{\pi}\times{}(6)^2\times{}h}$

$\implies\rm{36{\pi}h\:cm^3}$

$\hrulefill$

Clearly, Volume of sphere = Volume of cylinder

Therefore,

$\implies\rm{\dfrac{4\times{}4.2\times{}4.2\times{}4.2}{3}\pi=36{\pi}h}$

$\implies\rm{h=\dfrac{4\times{}4.2\times{}4.2\times{}4.2}{3\times{}36}}$

$\implies\rm{h=}\:\bold{2.74\:cm.}$

Hence, height of the cylinder is 2.74 cm.

Answer 2

Answer:

Step-by-step explanation:

Correct Question :-

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. find the height of the cylinder.

Answer :-

Given :-

Radius of sphere, r₁ = 4.2 cm

Radius of cylinder, r₂ = 6 cm

To Find :-

Height of cylinder, h = ??

Formula to be used :-

Volume of sphere = 4/3πr³

Volume of cylinder = πr²h

Solution :-

By comparing both,

Volume of sphere = Volume of cylinder

4/3πr₁³ = πr₂²h

⇒ 4/3r₁³ = r₂²h

⇒ 4/3 × 4.2 × 4.2 × 4.2 = 6 × 6 × h

⇒ h = 4 × 4.2 × 4.2 × 4.2/6 × 6 × 3

⇒ h = 296.352/108

⇒ h = 2.744 cm

Hence, the height of cylinder is 2.74 cm.