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A right circular cone is 3.6 cm high and radius of its base is 1.6 cm . It is melted and recast into a right circular cone with radius of its base as 1.2cm . Find its height .

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solution:  We have ,

                                      First cone                          Second cone 

Radii                              r_1= 1.6 cm                          r_2= 1.2 cm

Heights                          h_1=3.6 cm                            h_2=?

Volumes                              V_1                                 V_2

Clearly , Two cones have the same volume . i.e, 

                                   V_1 =V_2

Rightarrow                     frac13pi r^2_1h_1=frac13pi r^2_2h_2

Rightarrow                    r^2_1h_1=r^2_2h_2

Rightarrow                     h_2= fracr^2_1h_1r^2_2Rightarrow h_2=frac1.6	imes1.6	imes3.61.2	imes 1.2cm = frac16	imes16	imes3612	imes12	imes10=6.4cm

Posted by

Deependra Verma

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