A garden allotment's water butt is a cylinder with base radius \(35\) cm, shown in the diagram below. The manufacturer states that the water butt holds a vo...
Question 1 Report
A garden allotment's water butt is a cylinder with base radius \(35\) cm, shown in the diagram below. The manufacturer states that the water butt holds a volume of \(147\,000\pi\) cm\(^3\) when completely full.
Work out the height, \(h\), of the water butt in cm. (4)
Answer Details
The water butt is a cylinder, so its volume follows \(V=\pi r^{2}h\); since the volume and radius are both known, the formula can be rearranged to find the unknown height \(h\).
Writing down the cylinder volume formula: \(V=\pi r^{2}h\). [1 mark]
Substituting the known volume and radius: \(147\,000\pi=\pi(35)^{2}h\). [1 mark]
The \(\pi\) cancels from both sides, and \(35^{2}=1225\), leaving \(147\,000=1225h\). [1 mark]
Dividing both sides by 1225: \(h=\dfrac{147\,000}{1225}=120\) cm. [1 mark]
Writing the volume as a multiple of \(\pi\) in the question is a deliberate hint that the \(\pi\) will cancel exactly, leaving a clean whole-number height once the division is carried out.
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