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Question
The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cone of height 32 cm. Find the diameter of the base of the cone.
Solution
Internal radius = 3 cm
External radius = 5 cm
Volume of spherical shell
= `4/3pi(5^3 - 3^3)`
= `4/3 xx 22/7(125 - 27)`
= `4/3 xx 22/7 xx 98`
Volume of solid circular cone
= `1/3pir^2h`
= `1/3 xx 22/7 xx r^2 xx 32`
Vol. of cone = Vol. of sphere
`=> 1/3 xx 22/7 xx r^2 xx 32 = 4/3 xx 22/7 xx 98`
`=> r^2 = (4 xx 98)/32`
∴ `r = 2 xx 7/2`
∴ r = 7 cm
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