If a cube has an edge of 2 feet. The edge is increasing at the rate of 6 feet per minute. How would i express the volume of the cube as a function of m, the number of minutes elapsed. V(m)= ??

The volume of cube as function of m is,  

Let us consider that edge of cube is a feet.

Since,   The edge is increasing at the rate of 6 feet per minute.

Volume of cube , V =

Substituting the value of  da/dt in above equation.

We get,    

Integrating on both side.

Since, number of minutes elapsed is m.

Substitute , t = m and a = 2 feet in above equation.

We get,    

Thus, the volume of cube as function of m is,  

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v(m) = 8 + 48m+ 180m² +216m³

Step-by-step explanation:

Let's first of all represent the edge of the the cube as a function of minutes.

Initially the egde= 2feet

As times elapsed , it increases at the rate of 6 feet per min, that is, for every minute ,there is a 6 feet increase.

Let the the egde be x

X = 2 + 6(m)

Where m represent the minutes elapsed.

So we Al know that the volume of an edge = edge³

but egde = x

V(m) = x³

but x= 2+6(m)

V(m) = (2+6m)³

v(m) = 8 + 48m+ 180m² +216m³

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step-by-step explanation: