A cube has an edge of 4 feet. The edge is increasing at the rate of 3 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed

Answer: V = 144m + 64 Step-by-step explanation:The cube has an edge (a) = 4 feet. Now, the volume of the cube is given by V = a³ ....... (1) So, initially, the volume of the cube was 4³ =64 cubic feet. Now, differentiating equation (1) with respect to m (a variable which measurea number of minutes) we get [tex]\frac{dV}{dm} = 3a^{2} \frac{da}{dm} =3 \times 4^{2}  \times 3 =144[/tex]  {Since the rate of change of length of edge is 3 feet/ minutes} ⇒ [tex]dV = 144 \times dt[/tex] Integrating both sides we get, V = 144m + c {Where c is the constant of integration} ........ (2) Now, we know that at m = 0, V = 64 cubic feet. So, from equation (2), we get c = 64 Therefore, V = 144m + 64 .... this is the expression of V in terms of m. (Answer)