Edexcel C2 2005 June — Question 6

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2005
SessionJune
TopicArea Under & Between Curves

6. A river, running between parallel banks, is 20 m wide. The depth, \(y\) metres, of the river measured at a point \(x\) metres from one bank is given by the formula $$y = \frac { 1 } { 10 } x \sqrt { } ( 20 - x ) , \quad 0 \leqslant x \leqslant 20$$
  1. Complete the table below, giving values of \(y\) to 3 decimal places.
    \(x\)048121620
    \(y\)02.7710
  2. Use the trapezium rule with all the values in the table to estimate the cross-sectional area of the river. Given that the cross-sectional area is constant and that the river is flowing uniformly at \(2 \mathrm {~ms} ^ { - 1 }\),
  3. estimate, in \(\mathrm { m } ^ { 3 }\), the volume of water flowing per minute, giving your answer to 3 significant figures.