Answer:
(a).The volume of cube is changing at the rate [tex]450 cm^3/s[/tex]
Step-by-step explanation:
Let x be the side of cube
[tex]\frac{dx}{dt}=6 cm/s[/tex]
We have to find the rate at which volume of cube changing when edge is 5 cm.
We know that
Volume of cube, V=[tex]x^3[/tex]
Differentiate w.r.t t
[tex]\frac{dV}{dt}=3x^2\frac{dx}{dt}[/tex]
Substitute the values
[tex]\frac{dV}{dt}=3(5)^2\times 6[/tex]
[tex]\frac{dV}{dt}=450 cm^3/s[/tex]
Hence, the volume of cube is changing at the rate [tex]450 cm^3/s[/tex]
