Related rates: geometric models Problem set B Answers

21 cm² s⁻¹

126 cm² s⁻¹

0.0995 cm s⁻¹

1. (a) −4 cm² s⁻¹
2. (b) 2.92 cm s⁻¹

r = 5.97 cm

The top moves down at 0.375 m s⁻¹ (dy/dt = −0.375)

1.4 m s⁻¹

1. (a) Shown: \(V=\frac{\pi}{48}h^3\)
2. (b) dh/dt = 1.27 cm s⁻¹

0.0213 rad s⁻¹

Decreasing: the top of the quotient is negative

0.360 m s⁻¹