Figure 1 shows one side ABCD of a square-based prism. Each side of its square base is 14 cm, its height DC is 18 cm, and it is filled with water to a height of 16 cm. Figure 2 shows it tilted until the water level is MC, spilling some water. M is the midpoint of AB.
Find the volume of water spilled during the tilt.[2]
Find \(\angle CDE\), the angle between the prism and the table.[2]
The line \(L\) has equation \(2y-x=12\) and cuts the x-axis at \(Q\) and y-axis at \(P\).
Write down the gradient of \(PQ\).[1]
Point \(K\) lies on \(L\) and is equidistant from the x-axis and y-axis. Find all possible coordinates of \(K\).[2]
Find the acute angle \(QPO\).[2]
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Answer:(a)(i) \(490\text{ cm}^3\) (ii) \(57.3^\circ\) (b)(i) \(\frac12\) (ii) \((-4,4)\), \((12,12)\) (iii) \(63.4^\circ\)