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Paint spills onto a floor in a circular pattern. the radius of the spill increases at a constant rate of 2.5 inches per minute. how fast is the area of the spill increasing when the radius of the spill is 18 inches?
a) 5pi in^2/min
b) 36pi in^2/min
c) 45pi in^2/min
d) 90pi in ^2/min

Sagot :

Abiolataiwo2015idn

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.

Learn more about area of the spill here:ttps://brainly.com/question/3818648

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