Question

1. You are eating on a Tootsie Roll Lollipop that is in the shape of a sphere. It is giving up volume at a steady rate of 0.25 in3 /min. How fast will the radius be decreasing when the Tootsie Roll Pop is .75 inches across?

Answer 1

Explanation:

Since the Tootsie Roll lollipop is a sphere

volume of sphere=
`(4)/(3)piR^3` = -0.25
`in^3/min`

the negative sign indicates that the volume is decreasing

upon differentiating

as the diameter given is =0.75 so radius will be = 0.375

`dV/dt = 4piR^2*dR/dt`

so
`dR/dt = 0.25/4*3.14 *(0.375)^2`

So the radius is decreasing at the rate of dR/dt= 0.142in/min