If r is the radius of spherical balloon at time t and the surface area of balloon changes at a constant rate K, then ….

Question

If r is the radius of spherical balloon at time t and the surface area of balloon changes at a constant rate K, then …., 4 π r 2 = K t 2 2 + c, 8 π r 2 = K t + c, π r 2 = K t 2 2 + c, 4 π r 2 = K t + c

MARKS App · Accepted Answer

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

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