Question

the volume of a cube is decreasing at a rate of 0.24 ft^3/min. What is the rate of change of the side length when the side length are 2 feet.

Answer 1

ok what do we know

Answer 2

a^3=V

Answer 3

ko

Answer 4

ok

Answer 5

dV/da= 0.24 ft^3/min

Answer 6

ok

Answer 7

which also equals 3a^2

Answer 8

9a

Answer 9

? whered you get 9a

Answer 10

3a^2

Answer 11

sorry.. i dont follow

Answer 12

oh wait time has a place in this..sorry

Answer 13

dV/dt=3a^2(da/dt)

Answer 14

we have to solve for da/dt at a=2

Answer 15

do you follow?

Answer 16

well it looks like this

\[\frac{dV}{dt} = \frac{dV}{dx} \times \frac{dx}{dt}\]

you know

\[\frac{dV}{dt} = -0.24\]

you also know the volume of a cube side length x

\[V = x^3\]

then

\[\frac{dV}{dx} = 3x^2\]

so you know by substitution

\[-0.24 = 3x^2 \times \frac{dx}{dt}\]

substitiute x = 2 and solve for dx/dt

Answer 17

the units for the rate of change in the side length is ft/min

Answer 18

looks good

Answer 19

so then the answer would be -12.24