Answer to Question #272390 in Calculus for Fifi

Question

A storage tank has shape of a circular cylinder .Suppose that the radius and height of the tank are measured at 1.5 m and 5m respectively with a possible error in calculating the capacity of the tank

Answer 1

$$V=\pi r^2h$$

$$dV=2\pi r h dr+\pi r^2dh$$

$$\Delta V=\pi r (2 h\Delta r+ r\Delta h)$$

$$\Delta V=\pi(1.5)(2(5)(0.05)+(1.5)(0.1))$$

$$\approx 3.063({ft}^3)\approx3.1{ft}^3$$