MHT CET2019Morning ShiftMathematicsIndefinite IntegrationActual
If r is the radius of spherical balloon at time t and the surface area of balloon changes at a constant rate K, then ….
Options
- A4 π r 2 = K t 2 2 + c
- B8 π r 2 = K t + c
- Cπ r 2 = K t 2 2 + c
- D4 π r 2 = K t + c
Correct answer
D. 4 π r 2 = K t + c
Step-by-step solution
According to question, d d t 4 π r 2 = K ( ∵ surface area of spherical ballon with radius r is 4 π r 2 ) ⇒ 4 π 2 r d r d t = K ⇒ 8 π r d r = K d t On Integrating both sides, we get 8 π ∫ r d r = K ∫ d t ⇒ 8 π r 2 2 = K t + C ⇒ 4 π r 2 = K t + C