Question

when a circular plate of metal is heated in an oven, its radius increases at .03 cm/min, at what rate is the area increasing when the rate is 52 cm?

Answer 1

Rate of change of area will be
`9.796cm^2/min`

Step-by-step explanation:

We have given rate of change of radius
`(dr)/(dt)=0.03cm/min`

Radius of the circular plate r = 52 cm

Area is given by
`A=\pi r^2`

So
`(dA)/(dt)=2\pi r(dr)/(dt)`

Puting the value of r and
`(dr)/(dt)`

`(dA)/(dt)=2* 3.14* 52* 0.03=9.796cm^2/min`

So rate of change of area will be
`9.796cm^2/min`