CAIE P1 2021 November — Question 9 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionNovember
Marks3
TopicNon-constant acceleration

9 The volume \(V \mathrm {~m} ^ { 3 }\) of a large circular mound of iron ore of radius \(r \mathrm {~m}\) is modelled by the equation \(V = \frac { 3 } { 2 } \left( r - \frac { 1 } { 2 } \right) ^ { 3 } - 1\) for \(r \geqslant 2\). Iron ore is added to the mound at a constant rate of \(1.5 \mathrm {~m} ^ { 3 }\) per second.
[0pt]
  1. Find the rate at which the radius of the mound is increasing at the instant when the radius is 5.5 m . [3]
  2. Find the volume of the mound at the instant when the radius is increasing at 0.1 m per second.