Question

a solid cube is melted and recast into a cylinder with base radius equal to half of the edge of the cube . taking π=22/7, find the ratio of the height of cylinder to it's base radius is ?

Answer 1

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Answer 2

Hi there !!
Here's your answer

Let the edge of the cube be x units

Volume of the cube = x³ units

Given,
this cube is melted and recast into a cylinder with base radius equal to half of the edge of the cube.
Also,
we know that
Volume of cube = volume of cylinder

Radius of the base = x/2 units
Let the height be h

Volume = πr²h

${x}^{3} = \frac{22}{7} \times \frac{x}{2} \times \frac{x}{2} \times h$

${x}^{3} = \frac{22}{7} \times \frac{ {x}^{2} }{4} \times h$

$\frac{x {}^{3} \times 7 \times 4}{22 \times {x}^{2} } = h$
$h = \frac{14x}{11}$

to find the ratio of height to the base

Radius = x/2

Height = 14x/11

x/2 : 14x/11

$\frac{x}{2} \div \frac{14x}{11}$

$= \frac{x}{2} \times \frac{11}{14x}$

= 11/28


Thus,
the ratio is 11 : 28


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Hope it helps :D