Problema Solution
when a circular plate of metal is heated in an oven it's radius increases at a rate of 0.04cm/min. At what rate is the plate's area increasing when the radius is 46cm?
Answer provided by our tutors
We are given that the rate of change of the plate's radius dr/dt = 0.04 cm/min.
We are asked to find dA/dt, the rate of change of the plate's area, when the radius is r = 48 cm.
Now, the plate's area A is given by:
A = pi*r^2
So,
dA/dr = 2*pi*r
By the Chain Rule,
dA/dt = dA/dr dr/dt = (2*pi*r)(0.04) = 0.08*pi*r
Plug r = 46 cm into the equation:
dA/dt = 0.08*pi*46
dA/dt = 3.68*pi cm^2/min
dA/dt = 11.56 cm^2/min (approximately)
The plate's area is increasing by the rate of 11.56 cm^2/min.