p.206, problem 15

A spherical Tootsie Roll pop you are sucking on is giving up volume at a steady rate of 0.08mL/min . How fast will the radius be decreasing when the Tootsie Roll pop is 20mm across?

Assume that the rate will be negative, since the values (dV/dt) will be decreasing

dV = 0.08mL/min

0.08mL = ?mm

when 1mL = 10mm so 0.08 X 10 = 0.8mm

dV = 0.8mm/min

solve for dr/dt

when d = 20mm, r = 10mm

V = (4/3)πr³

• step one: take the derivative of the volume formula

dV/dt = 4πr²(dr/dt)

• step two: plug in known values

0.8 = 4π(10)²(dr/dt)

• step three: solve for dr/dt

0.8 = 4(100)π(dr/dt)

0.8 = 400π(dr/dt)

0.002π = dr/dt

dr/dt = 0.00628mm/min