1.

A hollowsphere of internal and external diameters 4 cm and 8 cm respectively ismelted into a cone of base diameter 8 cm. Calculate the height of the cone.

Answer» External radius of the sphere = 4 cm
Internal radius of the sphere = 2 cm
Volume of the material of the sphere `= (4)/(3) pi (4^(3) - 2^(3)) cm^(3)`
`= ((224pi)/(3)) cm^(3)`
Radius of the resulting cone, r = 4cm
Let the height of this cone formed be h cm
Volume of the cone `= ((1)/(3) pir^(2)h) cm^(3)`
`= ((1)/(3) pi xx 4 xx 4 xx h) cm^(3) = ((16pih)/(3)) cm^(3)`
`:. (16pih)/(3) = (224pi)/(3) rArr h = ((223)/(3) xx (3)/(16)) = 14`
Hence, the height of the cone is 14 cm


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