The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 60 mm?

22608 mm³/s

Step-by-step explanation:

Applying chain rule,

dV/dt = (dV/dr)(dr/dt) Equation 1

Where dV/dr = rate at which the volume is increasing

But,

V = 4πr³/3

Therefore,

dV/dr = 4πr² Equation 2

Substitute equation 2 into equation 1

dV/dt = 4πr²(dr/dt) Equation 3

From the question,

Given: dr/dt = 2 mm/s, r = 60/2 = 30 mm

Consatant: π = 3.14

Substitute these values into equation 3

dV/dt = 4×3.14×30²×2

dV/dt = 22608 mm³/s

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total