rates of change (1 Viewer)

[want2beSMART]

a cube is expanding so that its side is increasing at the constant rate of 0.12 mms^-1. find the rate of increase in its volume when its side is 150mm

 

[shafqat]

a cube is expanding so that its side is increasing at the constant rate of 0.12 mms^-1. find the rate of increase in its volume when its side is 150mm

dx/dt = 0.12 (given)
V = x^3
dV/dx = 3x^2
so dV/dt = dV/dx * dx/dt
= 3x^2 * 0.12
= 3(150)^2*0.12 when the side is 150
= 8100 mm^3/s

 

[want2beSMART]

why it is dx/dt = 0.12 and not dV/dt = 0.12?

 

[shafqat]

well its SIDE (ie x) is increasing at a rate of 0.12, not its VOLUME (V)
so dx/dt (the rate of change of the side) = 0.12

 

[want2beSMART]

oh i see

thanks a lot man

you went to sgs? do you know brian stoppa?