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What will be the height of the cone of r...

What will be the height of the cone of radius 12 cm if a solid cone is made by melting a solid coneof radius of base 6 cm and of slant height 10 cm ?

Text Solution

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The radius of the base of the first right circular cone = 6cm and slant height = 10 cm.
`therefore` the height of the right circular cone `=sqrt((10)^2-(6)^2)cm=8cm`
`therefore ` volume of the cone `=(1)/(3)pi xx 6^2xx8` cm -cm.
The new radius of the cone is 12 cm and the height is h cm , the volume of the cone `=(1)/(3)pi xx(12)^2xxh` cubic - cm.
As per question, `(1)/(3)pi xx912)^2xxh=(1)/(3)pi xx (6)^2xx8rArr h =(6xx6xx8)/(12xx12)=2`.
Hence the height of the new cone `=2cm`.
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