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.
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.
Comment