Question

the volume of a cube is increasing at a rate of 9 cubic centimeters per second. how fast is the surface area increasing when the length of an edge is 10 centimeter?

Answer 1

V=L^3
defferentiate w.r.t time
dV/dt= 3L^2.dL/dt
given ,
dV/dt=9 cm^3/s
L=10cm
hence dL/dt =9/300=3/100 cm/s
now ,
surface area of cube(A)=6 x L^2
A=6L^2
differentiate w.r.t time
dA/dt =12L.dL/dt
=12 x 10 x 3/100=3.6 cm^2/s

Answer 2

Answer:

3.6 cm²/sec

Step-by-step explanation:

→ V = x³                                      V : Volume of the cube of side x

→ dv / dt = 3x² dx/dt                S :- Surface area of the cube of side x

→ 3 A = 3 (x²) dx/dt

→ dx / dt = 3 / x²

   S = 6x²

→ ds / dt = 12x dx / dt

           = 12 x (3 / x²)

             = 36 / x

→ ds / dt | x = 10 cm

                = 36 / 10 cm² / sec

  = 3.6 cm² / sec

Good luck !!