[High School - Calculus AB] Related Rates

180digi · 01-8-2009, 08:29 PM

Please tell me if I have done this correctly.

8) Heating a Plate

When a circular plate of metal is heated in an oven, its radius increases at the rate of .01cm/sec. At what rate is the plate's area increasing when the radius is 50cm?

First I drew a picture of a circle with r=50cm. My knowns are r=50cm and dr/dt=.01cm/s.

I use circumference and area formulae to relate: C=2(pi)r and A=(pi)r^2. I differentiate both sides of the area formula.

dA/dt= 2(pi)r(dr/dt). I plug in my knowns.

dA/dt = 2(pi)(50cm)(.01cm/s). I get 3.141592...cm^2/s or the plate's area increases by pi centimeters squared per second.

Thank you.

**MeaCulpa** · 01-8-2009, 08:42 PM

Yep, you're good.

01-8-2009, 08:29 PM	#1
180digi FFR Player Join Date: May 2004 Location: I'm a computer. Age: 33 Posts: 969	[High School - Calculus AB] Related Rates Please tell me if I have done this correctly. 8) Heating a Plate When a circular plate of metal is heated in an oven, its radius increases at the rate of .01cm/sec. At what rate is the plate's area increasing when the radius is 50cm? First I drew a picture of a circle with r=50cm. My knowns are r=50cm and dr/dt=.01cm/s. I use circumference and area formulae to relate: C=2(pi)r and A=(pi)r^2. I differentiate both sides of the area formula. dA/dt= 2(pi)r(dr/dt). I plug in my knowns. dA/dt = 2(pi)(50cm)(.01cm/s). I get 3.141592...cm^2/s or the plate's area increases by pi centimeters squared per second. Thank you. __________________ You'll never walk alone.

01-8-2009, 08:42 PM	#2
MeaCulpa FFR Simfile Author Join Date: Jan 2007 Location: T-Dot Age: 35 Posts: 841	Re: [High School - Calculus AB] Related Rates Yep, you're good.

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