<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">A certain machine \(A\) is pumping a liquid into an empty container of total volume \(850\) m\({}^3\). The first pumping action fills the container with a volume of \(4\) m\({}^3\). Each subsequent pumping action fills the container with \(0.5\) m\({}^3\) more than the previous pumping action. Pumping continues until the container is completely filled with the liquid. Find the volume of liquid that overflows from the container at the final pumping action.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Suppose that, after the \(50\)th pumping action by machine \(A\), a different machine \(B\) is used instead to fill the remaining volume of the container. Using machine \(B\), the first pumping action fills the container with a volume of \(5\) m\({}^3\). Each subsequent pumping action fills the container with \(\frac{5}{6}\) the amount filled in the previous pumping action.</div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the total volume of the container filled after the \(10\)-th pumping action by machine \(B\).</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Explain whether the container would be completely filled eventually.</span><span class="inline-marks">[2]</span></div></li></ol></li></ol>

A certain machine \(A\) is pumping a liquid into an empty container of total volume \(850\) m\({}^3\). The first pumping action fills the container with a volume of \(4\) m\({}^3\). Each subsequent pumping action fills the container with \(0.5\) m\({}^3\) more than the previous pumping action. Pumping continues until the container is completely filled with the liquid. Find the volume of liquid that overflows from the container at the final pumping action.

Suppose that, after the \(50\)-th pumping action by machine \(A\), a different machine \(B\) is used instead to fill the remaining volume of the container. Using machine \(B\), the first pumping action fills the container with a volume of \(5\) m\({}^3\). Each subsequent pumping action fills the container with \(\frac{5}{6}\) the amount filled in the previous pumping action.

Suppose that, after the \(50\)th pumping action by machine \(A\), a different machine \(B\) is used instead to fill the remaining volume of the container. Using machine \(B\), the first pumping action fills the container with a volume of \(5\) m\({}^3\). Each subsequent pumping action fills the container with \(\frac{5}{6}\) the amount filled in the previous pumping action.

Find the total volume of the container filled after the \(10\)-th pumping action by machine \(B\).

2013 CJC P2 Q1

2013 CJC P2 Q1