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Conversion of Solid from One Shape to Another

notes

Now let's understand on what principle the conversion of Solid from One Shape to Another depends. Let's take example of a wax candle.

This candle is of cylindrical shape with a distinct height and distinct radius. If further the candle is kept in cylinder jar and melted,

wax will melt down. And once it is allowed to cool the wax candle will change into different shape. The new candle is different from the first candle, it will be more thick and it will have less height. The amount of wax is same in both cases.

i.e Volume before molding= Volume after molding

Example 1: A cone of height 24 cm and radius of base 6 cm is made up of modeling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

Solution : Volume of cone = `1/3 pi r^2h`

If r is the radius of the sphere, then its volume is `4/3 pi r^3`

Since, the volume of clay in the form of the cone and the sphere remains the same, we have

`4/3 pi r^3`  = `1/3 pi r^2h`

 

`4/3 pi r^3`  =`1/3 pi xx 6 xx 6 xx 24`

 

`r^3`        = `3 xx 3 xx 24= 3^3 xx 2^3`

 

`r= 3 xx 2= 6`

Therefore, the radius of the sphere is 6 cm.

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Shaalaa.com | Surface Area and Volume part 11 (Shape Conversion Example)

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Surface Area and Volume part 11 (Shape Conversion Example) [00:08:18]
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