Related Rates 2

Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100π ft?

What equation(s) should be used?

• $A=πr^2\ \ and\ \ C=2πr$

• $C=2πr$

• $A=πr^2$

• $A=πr^2\ \ and\ \ \ C\ =πd$

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.GMD.A.1

Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100π ft?

What rate is given in the problem?

•  $\frac{dC}{dt}=40$ 

•  $\frac{dr}{dt}=40$ 

•  $\frac{dA}{dt}=40$ 

•  $\frac{dπ}{dt}=40$ 

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100π ft?

What rate are we looking for and when?

•  $\frac{dA}{dt}\ when\ C=100π$ 

•  $\frac{dC}{dt}\ when\ A\ =\ 100π$ 

•  $\frac{dA}{dt}\ when\ A\ =\ 100π$ 

•  $\frac{dC}{dt}\ when\ r\ =\ 100π$ 

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.4

What is the derivative of circumference with respect to time?

• $\frac{dC}{dt}=2π\cdot\frac{dr}{dt}$

• $\frac{dC}{dt}=2π$

• $\frac{dC}{dt}=2πr$

• $\frac{dC}{dt}=π\cdot\frac{dr}{dt}$

Tags

CCSS.HSG.GMD.A.1

What is the derivative of area with respect to time?

• $\frac{dA}{dt}=2πr\cdot\frac{dr}{dt}$

• $\frac{dA}{dt}=2πr$

• $\frac{dA}{dt}=πr\cdot\frac{dr}{dt}$

• $\frac{dA}{dt}=πr^2\cdot\frac{dr}{dt}$

Tags

CCSS.HSF.BF.A.1

Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100π ft?

What is the length of the radius when the circumference is 100π ft?

•  $r=50\ ft$ 

•  $r=100\ ft$ 

•  $r=\sqrt{50}ft$ 

• cannot be determined

Tags

CCSS.HSG.GMD.A.1

CCSS.HSA.SSE.A.1

Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100π ft?

At what rate is the radius changing when the circumference is 100π ft?

•  $\frac{dr}{dt}=\frac{20}{π}$ 

•  $\frac{dr}{dt}=\frac{50}{π}$ 

•  $\frac{dr}{dt}=50$ 

•  $\frac{dr}{dt}=20$  

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.GMD.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.CED.A.1

Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100π ft?

•  $\frac{dA}{dt}=2000\ \frac{ft^2}{\sec}$ 

•  $\frac{dA}{dt}=40\ \frac{ft^2}{\sec}$ 

•  $\frac{dA}{dt}=100\ \frac{ft^2}{\sec}$ 

•  $\frac{dA}{dt}=200\ \frac{ft^2}{\sec}$  

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.GMD.A.1

CCSS.HSA.SSE.A.1