Answer:
24 in³ per sec.
Step-by-step explanation:
Since, the volume of a cube ,
[tex]V = x^3-----(1)[/tex]
Where,
x = side length,
Differentiating equation (1) w. r. t ( time ),
[tex]\frac{dV}{dt}=3x^2 \frac{dx}{dt}[/tex]
Here,
[tex]x = 4\text{ in},\frac{dx}{dt}= 0.5\text{ in per sec}[/tex]
[tex]\implies \frac{dV}{dt}=3(4)^2(0.5) = 24\text{ cube in per sec}[/tex]
That is, volume of the cube is changing with the rate of 24 in³ per sec.
