A container is in the shape of a cylinder of height \(10\text{ cm}\) with a conical top of height \(2\text{ cm}\). The base of the container has a diameter of \(3\text{ cm}\).
Calculate the volume of the container correct to 3 significant figures.[3]
75% of the container is filled with water. Calculate the depth, \(d\text{ cm}\), of the empty space in the container.[3]
All the liquid is transferred to fill up a square-based pyramid completely in \(x\) minutes. Find the height of the pyramid if the side of the base is \(4\text{ cm}\).[2]
Find the time taken, in terms of \(x\), for the liquid to fill up to \(\dfrac13\) of the height of the square pyramid in (c).[1]