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Question
The total area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate :
- the radius of the solid sphere.
- the number of cones recast. [Take π = 3.14]
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Solution
Total area of solid metallic sphere = 1256 cm2
i. Let radius of the sphere is r then
4πr2 = 1256
`=> 4 xx 22/7r^2 = 1256`
`=> r^2 = (1256 xx 7)/(4 xx 22)`
`=> r^2 = (157 xx 7)/11`
`=> r^2 = 1099/11`
`=> r = 1099/11`
`=> r = sqrt(99.909) = 9.995 cm`
`=>` r = 10 cm
ii. Volume of sphere = `4/3pir^3`
= `4/3 xx 22/7 xx 10 xx 10 xx 10`
= `88000/21 cm^3`
Volume of right circular cone = `1/3pir^2h`
= `1/3 xx 22/7 xx (2.5)^2 xx 8`
= `1100/21 cm^3`
Number of cones
= `88000/21 ÷ 1100/21`
= `88000/21 xx 21/1100`
= 80
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