How fast is the area of the spill increasing when the radius of the spill is 18 inches is d) 90pi in ^2/min.
Area of the spill
Area of the spill=S=πr²
dS/dr=(πr²)=2πr
Radius change with speed=dr/dt =2.5(m/s)
Area of the spill will increase with speed
dS/dt = dS/dr × dr/dt =2πr ×dr/dt
=2π×18×2.5
=282.74m²/s or 90pi in²/min
Therefore the correct option is D.
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