Question

When a circular plate of metal is heated in an​ oven, its radius increases at a rate of 0.04 cm divided by min. At what rate is the​ plate's area increasing when the radius is 43 ​cm?

Answer 1

Answer:

The plate's area is increasing at the rate of 10.81 cm²/min when the radius is 43 cm.

Step-by-step explanation:

The area of a circle is given by the following formula:

$A = \pi r^{2}$

In which the area is measured in cm².

Its radius increases at a rate of 0.04 cm divided by min.

This means that $\frac{dr}{dt} = 0.04$

At what rate is the​ plate's area increasing when the radius is 43 ​cm?

This is $\frac{dA}{dt}$ when $r = 43$

$A = \pi r^{2}$

Applying implicit differentitation

We have two variables(A and r), so

$\frac{dA}{dt} = 2r\pi \frac{dr}{dt}$

$\frac{dA}{dt} = 2*43\pi*0.04$

$\frac{dA}{dt} = 10.81$

The plate's area is increasing at the rate of 10.81 cm²/min when the radius is 43 cm.