The volume of a cylindrical tank varies with time according to

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The volume of a cylindrical tank varies with time according to V(t)=π r(t)2h(t)V(t)=\pi\,r(t)^{2}h(t), where the radius and height change with time as follows: r(t)=2+0.1sin⁡t meters,h(t)=5e0.05t meters.\displaystyle r(t)=2+0.1\sin t\ \text{meters}, \qquad h(t)=5e^{0.05t}\ \text{meters}. Calculate dVdt\dfrac{dV}{dt} (in cubic meters per second) at t=πt=\pi.

Related theory

Browse the problem library