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ఎల్లప్పుడూ గోళాకారంగా ఉండే గాలిబుడగ, అస్థిరమైన వ్యాసం కలిగి ఉంటుంది. xకి సంబంధించి దాని ఘన పరిమాణము యొక్క మార్పు రేటును కనుగొనండి.

  1. 12π R2
  2. 4π R2​
  3. 3π R2​
  4. 6π R2​

Answer (Detailed Solution Below)

Option 1 : 12π R2

Detailed Solution

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లెక్కింపు: 

గోళాకారంగా ఉండే  గాలిబుడగ యొక్క ఇవ్వబడిన వ్యాసం D=

వ్యాసార్థము R=

వ్యాసార్థం యొక్క మార్పు రేటు R wrt x==

=

==3

గోళాకారంగా ఉండే  గాలిబుడగ యొక్క ఘన పరిమాణము V=

వ్యాసార్థం యొక్క మార్పు రేటు V wrt x==

=
 
== 12πR2 

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