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CBSE Class 10 Answered

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted and cast into a cone of base diameter 8 cm. Find the height of the cone.
Asked by Topperlearning User | 27 Oct, 2017, 03:00: PM
answered-by-expert Expert Answer

External diameter of sphere = 8 cm rightwards double arrowradius, R = 4 cm

Internal diameter of sphere = 4 cm rightwards double arrowradius, r = 2 cm

Diameter of the base of cone = 8 cm rightwards double arrowradius = 4 cm

Now, Volume of the cone = Volume of the material in the sphere

rightwards double arrow 1 third straight pi left parenthesis 4 right parenthesis squared straight h equals 4 over 3 straight pi left parenthesis straight R cubed minus straight r cubed right parenthesis
rightwards double arrow 16 straight h equals 4 left parenthesis 4 cubed minus 2 cubed right parenthesis
rightwards double arrow straight h equals fraction numerator 4 cross times 56 over denominator 16 end fraction equals 14 space cm

Hence, the height of the cone = 14 cm      


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