An ink blot has an area that is increasing at 8mm^2/s at what rate is the diameter increasing at this time

Answer 1

Given

Incresing rate of the area,dA/dt  = 8 mm/s²

Write the formula for area of the ink blot,

A = (π/4)d²

Area is not given.

Substitute area value to find d.

Derivative both sides with respect to t .

A = (π/4)d²

A' = π/4 (2d d')

A' = (π/2 )(d d')

d' =2A'/πd

Substitute 8 mm/s² for A'.

d' =2(8)/πd

  = 5.09 /d   mm/s

Not given diameter .

Therefore, the increasing rate of the diameter is 5.09 /d mm/s