A right circular cone is 5.4cm high and the radius of its base is 2cm. It is melted and recast into another right circular one with a radius of base as 1.5 cm. find the height of the new cone formed.

Volume of the old cone = volume of the new cone

\(\frac{1}{3} \pi \times r_{1}^{2} h_{1}=\frac{1}{3} \pi \times r_{2}^{2} h_{2} \\ r_{1}^{2} h_{1}=r_{2}^{2} h_{2} \\ 2^{2} \times 5.4=(1.5)^{2} \times h_{2} \\ h_{2}=\frac{4 \times 5.4}{2.25}=\frac{21.6}{2.25} \\ h_{2}=9.6 \mathrm{~cm}\)

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