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Question
Find the diameter of the sphere for the following :
Volume = `72pi "cm"^3`
Solution
Volume = `72pi "cm"^3`
Volume of sphere = `4/3pir^3 = 72pi`
⇒ `4/3pir^3 = 72pi`
⇒ `4/3 xx r^3 = 72`
⇒ `r^3 = (72 xx 3)/4 = 216/4`
⇒ `r^3 = 54`
⇒ `r = 3 root(3)(2)` cm
Radius = `3 root(3)(2)` cm `3 root(3)(2)` ⇒ Diameter = 2r = `6 root(3)(2)` cm `root(3)(2)`
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