Related rates: geometric models Problem set A Answers

48 cm² s⁻¹

12.6 m² per minute

0.531 cm s⁻¹

1. (a) 18 cm² s⁻¹
2. (b) 1 cm s⁻¹

r = 6.37 cm

The top moves down at 0.250 m s⁻¹ (dy/dt = −0.25)

3.2 m s⁻¹

1. (a) Shown: \(V=\frac{4\pi}{75}h^3\)
2. (b) dh/dt = 0.637 cm s⁻¹

0.0446 rad s⁻¹

Increasing: the top of the quotient is positive

0.267 m s⁻¹