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Related Rates Date Period - cdn.kutasoftware.com

F j2I0n1u3h MKRuat8aD mSNowfVtzwjaKrQe6 H fADlPlu 9rwiEgHhntzsL 9 XMGasdFew Tw8iztchh 9 IYnXfri7nMiVtveS by Kuta Software LLCKuta Software - Infinite CalculusName_____ Period____Date_____Related RatesSolve each Related rate ) Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 5 cm?2) Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The area ofthe spill increases at a rate of 9 m /min. How fast is the radius of the spill increasing when theradius is 10 m?

Related Rates Date_____ Period____ Solve each related rate problem. 1) Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 5 cm? 2) Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean.

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Transcription of Related Rates Date Period - cdn.kutasoftware.com

1 F j2I0n1u3h MKRuat8aD mSNowfVtzwjaKrQe6 H fADlPlu 9rwiEgHhntzsL 9 XMGasdFew Tw8iztchh 9 IYnXfri7nMiVtveS by Kuta Software LLCKuta Software - Infinite CalculusName_____ Period____Date_____Related RatesSolve each Related rate ) Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 5 cm?2) Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The area ofthe spill increases at a rate of 9 m /min. How fast is the radius of the spill increasing when theradius is 10 m?

2 3) A conical paper cup is 10 cm tall with a radius of 10 cm. The cup is being filled with water sothat the water level rises at a rate of 2 cm/sec. At what rate is water being poured into the cupwhen the water level is 8 cm?-1- q M2y0b1z39 fKTuqt6aI lSLoEf1tow6a9rieQ X dAgl4lJ drIi2g2hgtFsW 1 pMua3dyem vwQi2tBhJ TIRn0fpi7nXictOej by Kuta Software LLC4) A spherical balloon is inflated so that its radius ( r) increases at a rate of 2 r cm/sec. How fast isthe volume of the balloon increasing when the radius is 4 cm?5) A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume thescenario can be modeled with right triangles.

3 At what rate is the length of the person's shadowchanging when the person is 16 ft from the lamppost?6) An observer stands 700 ft away from a launch pad to observe a rocket launch. The rocketblasts off and maintains a velocity of 900 ft/sec. Assume the scenario can be modeled as a righttriangle. How fast is the observer to rocket distance changing when the rocket is 2400 ft fromthe ground?-2- 2 y2q0d1G34 cKKultUaW ySWokfxtKwzamrHeJ I pA3lclb prniogMhUtOs4 S zMBa8dgen kw9iftehQ AIPnJfRignUiQtQes by Kuta Software LLCKuta Software - Infinite CalculusName_____ Period____Date_____Related RatesSolve each Related rate ) Water leaking onto a floor forms a circular pool.

4 The radius of the pool increases at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 5 cm? A = area of circle r = radius t = timeEquation: A = r2 Given rate: dr dt = 4 Find: dA dt r = 5 dA dt r = 5 = 2 r dr dt = 40 cm /min2) Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The area ofthe spill increases at a rate of 9 m /min. How fast is the radius of the spill increasing when theradius is 10 m? A = area of circle r = radius t = timeEquation: A = r2 Given rate: dA dt = 9 Find: dr dt r = 10 dr dt r = 10 = 12 r dA dt = 920 m/min3) A conical paper cup is 10 cm tall with a radius of 10 cm.

5 The cup is being filled with water sothat the water level rises at a rate of 2 cm/sec. At what rate is water being poured into the cupwhen the water level is 8 cm? V = volume of material in cone h = height t = timeEquation: V = h33 Given rate: dh dt = 2 Find: dV dt h = 8 dV dt h = 8 = h2 dh dt = 128 cm /sec-1- f 72F0g1f3z XK5untPaA xS7okfytNwOa7rKeh M GAIlelf erfiHgThXtGs1 6 yM8a6dLel fw6ibt6hv DIAnbfgiInTiktveN by Kuta Software LLC4) A spherical balloon is inflated so that its radius ( r) increases at a rate of 2 r cm/sec. How fast isthe volume of the balloon increasing when the radius is 4 cm?

6 V = volume of sphere r = radius t = timeEquation: V = 43 r3 Given rate: dr dt = 2 r Find: dV dt r = 4 dV dt r = 4 = 4 r2 dr dt = 32 cm /sec5) A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. Assume thescenario can be modeled with right triangles. At what rate is the length of the person's shadowchanging when the person is 16 ft from the lamppost? x = distance from person to lamppost y = length of shadow t = timeEquation: x + y20 = y7 Given rate: dx dt = 5 Find: dy dt x = 16 dy dt x = 16 = 713 dx dt = 3513 ft/sec6) An observer stands 700 ft away from a launch pad to observe a rocket launch.

7 The rocketblasts off and maintains a velocity of 900 ft/sec. Assume the scenario can be modeled as a righttriangle. How fast is the observer to rocket distance changing when the rocket is 2400 ft fromthe ground? a = altitute of rocket z = distance from observer to rocket t = timeEquation: a2 + 490000 = z2 Given rate: da dt = 900 Find: dz dt a = 2400 dz dt a = 2400 = a z da dt = 864 ft/sec-2-Create your own worksheets like this one with Infinite Calculus. Free trial available at


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