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

A. `4pir^(2)=(Kt^(2))/(2)+c`
B. `8pir^(2)=Kt+c`
C. `pir^(2)=(Kt^(2))/(2)+c`
D. `4pir^(2)=Kt+c`

Answer

D

Explanation

According to question,
`(d)/(dt)(4pir^(2))=K" "(becacuse" surface area of spherical balloon with radius r is "4pir^(2))`
`implies4pi(2r)(dr)/(dt)=Kimplies8pir" "dr=kdt`
On integrating both sides, we get
`8pi int r dr =K int dt`
`implies8pi(r^(2))/(2)=Kt+C`
`implies4pir^(2)=Kt+C`