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A solid metallic hemisphere of radius 8 cm is melted and re casted into a right circular cone of base radius 6 cm. Determine the height of the cone.

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Answer h = 28.44 cm


Radius of hemisphere =8cm


\frac{2}{3}\times\pi r^3


Radius of cone = 6 cm

Let height = h

Volume =  \frac{1}{3}\times\pi r^2h = \frac{1}{3}\times\frac{22}{7}\times6\times6\times h

If hemisphere is melted and recast into a right circular cone.

Then, the volume of hemisphere = volume of the cone

\frac{2}{3}\times\frac{22}{7}\times8\times8\times8 = \frac{1}{3}\times\frac{22}{7}\times6\times6\times h


2\times8\times8\times8 = \times6\times6\times h

\frac{2\times8\times8\times8 }{6\times6}= h

\frac{256 }{9}= h

28.44 = h

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