Question

The volume of a cube is increasing at the rate of 8 cm 3 /s. How fast is the surface area increasing when the length of an edge is 12 cm?

Answer 1

Given dv/dt =8cm^3/s
v=a^3 here a is side length
dv/dt=3a^2.da/dt=8
So,da/dt=8/3a^2
Surface area of cube(s)=4a^2
ds/dt=8a.da/dt=8a.8/3a^2=64/3a=64/3(12)=16/9 cm^2/s