Question

9. A solid sphere of radius 5.6 cm is melted and recast into a cylinder of radius 8 cm, then find the height of
the cylinder.

Answer 1

Given :-

A solid sphere of radius 5.6 cm is melted and recast into a cylinder of radius 8cm.

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To Find :-

The height of the cylinder.

Solution

Radius of solid Sphere = 5.6 cm.

✳ When an object of one shape is melted and recast into another shape , it's volume remains the same.

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

Here,

r = 5.6

$\implies \sf Volume \: of \:the\: sphere = \dfrac{4}{3} \pi * 5.6 * 5.6 *5.6$

$\implies \sf Volume \: of \:the\: sphere = \dfrac{4}{3} \pi * 175.616$

$\implies \sf Volume \: of \:the\: sphere = 4\pi * 58.5 (Approximately)$

$\implies \sf Volume \: of \:the\: sphere = 234\pi (Approximately)$$\longrightarrow$(1)

Volume of a cylinder = πr²h

Here,

r = 8cm.

$\implies$ Volume of the cylinder = π × 8² × h

$\implies$ Volume of the cylinder = 64π × h $\longrightarrow$(2)

Now , ∵ Volume of Cylinder = Volume of Sphere Let us substitute (1) and (2).

$\implies$ 234 π = 64π × h

( π and π gets cancelled)

$\implies$ 234 = 64h

$\implies \sf h = \dfrac{234}{64}$

$\implies$ h = 3.65(Approximately)