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प्रश्न
Write True or False and justify your answer in the following.
A solid ball is exactly fitted inside the cubical box of side b, The volume of ball is `4/3 πb^3`.
औचित्य
चूक किंवा बरोबर
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उत्तर
This statement is false.
Explanation:
If the sphere is exactly fitted inside the cube of side b then its diameter = b, so `r = b/2`.
The sphere volume is `V = 4/3 πr^3`.
So, `V = 4/3 π(b/2)^3`
= `4/3 π(b^3/8)`
= `4/24 πb^3`
= `1/6 πb^3`
Thus, the correct volume is `1/6 πb^3`, not `4/3 πb^3`.
The sphere volume formula used above is `V = 4/3 πr^3`.
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