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Question
A hollow metallic sphere is 2 cm thick all around and has an external diameter of 12 cm. Find the radius of the solid sphere made by recasting this hollow sphere.
Solution
External diameter of hollow sphere = 12 cm
External radius = R = 6 cm
Internal diameter of hollow sphere = ( 12 - 4) cm= 8 cm
Internal radius = r = 4 cm
Volume of metal used = `4/3pi(R^3 - r^3)`
= `4/3 xx 22/7 xx (6^3 - 4^3)`
= `4/3 xx 22/7 xx 152`
= 636.95 `"cm"^3`
Volume of metal used = 636.95 cm3 = volume of sdid sphere
⇒ `4/3pir^3 = 636.95`
⇒ `4/3 xx 22/7 xx r^3 = 636.95`
⇒ `r^3 = (636.95 xx 3 xx 7)/(4 xx 22)`
⇒ `r^3 = 151.99 = 152`
⇒ r = 5.34 cm
Radius of the solid sphere = 5.34 cm
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