All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the volume changing when each edge is 2 centimeter(s)?
(b) How fast is the volume changing when each edge is 14 centimeter(s)?

The volume will be:

(a) 24 cm³

(b) 1176 cm³

Given:

Expanding rate,

Let,

(a)

When,

then,

→

Let,

→

→

(b)

When,

then,

→

Let,

→

→

Thus the above answer is correct.

Learn more about cube here:

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Step-by-step explanation:

As all edges of a cube are expanding at a rate of 2 centimeters per second.

i.e ds/dt = 2 cm/s

The formula of volume of cube: V = s³

Differentiating the volume:

dv/dt = 3s²

Write ds/dt following derivative of volume

dv/dt = 3s² ds/dt

plug in the value: ds/dt = 2 cm/s

dv/dt = (3s²) (2)

dv/dt = 6s²

Given the edge is 2cm.

so plug in the value: s=2

dv/dt = 6s²

          = 6(2)²=6(4)=24 cm³/per second

SIMILARLY,

When the edge is 14cm

dv/dt = 6s²

plug in the value: s=14

dv/dt = 6s²

         = 6(14)²=6(196)=1176 cm³/per second

Thus,

your answer would be 12