Edexcel Mathematics October 2020 · Paper 1 · Question 14 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

October 2020 · Paper 1 · Question 14 · 10 marks

14. A large spherical balloon is deflating. At time t seconds the balloon has radius r cm and volume V cm3 The volume of the ball oon is modelled as decreasing at a constant rate. (a) Using this model, show that d dr t = −k r2 where k is a positive constant. (3) Given that ● the initial radius of the balloon is 40 cm ● after 5 seconds the radius of the balloon is 20 cm ● the volume of the balloon continues to decrease at a constant rate until the balloon is empty (b) solve the dif ferential equation to find a complete equation linking r and t. (5) (c) Find the limitation on the values of t for which the equation in part (b) is valid. (2) 43 44 45