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प्रश्न
A hollow sphere of internal and external radii 2cm and 4cm is melted into a cone of basse radius 4cm. find the height and slant height of the cone______?
उत्तर
Given that internal radii of hollow sphere (r) = 2cm
External radii of hollow sphere (R) = 4cm
Volume of hollow sphere = `4/3pi(R^2-r^2)`
`v_1=4/3xxpi(4^2-2^2)` ..........(1)
Given that sphere is melted into a cone
Base radius of cone = 4cm
Let slant height of cone be l
Let height of cone be h
`l^2=r^2+h^2`
`l^2=16+h^2` ..............(3)
Volume of cone`=1/3pir^2h`
`v_2=1/3pi(4)^2h` .................(2)
v1 = v2 Equating (1) and (2)
`4/3pi(4^2-2^2)=1/3pi(4)^2h`
`(4/3pi(16-4))/(1/3pi(16))=h`
h = 14cm
Substituting ‘h’ value in (2)
`l^2=16+h^2`
`l^2=16+14^2`
l2 = 16 + 196
l = 14.56cm
∴ Slant height of cone = 14.56cm
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