A workshop makes closed cylindrical drums for a transport depot. Each drum has radius \(6\) cm and height \(14\) cm. Calculate the total surface area of one...
Question 1 Report
A workshop makes closed cylindrical drums for a transport depot. Each drum has radius \(6\) cm and height \(14\) cm. Calculate the total surface area of one drum, correct to 3 significant figures. (3)
Answer Details
A closed cylinder has three surfaces: two circular ends and one curved surface. Imagine unrolling the curved surface: it becomes a rectangle whose width is the circumference \(2\pi r\) and whose height is \(h\), which is why its area is \(2\pi r h\).
- Two circular ends: \(2 \times \pi \times 6^2 = 2 \times 36\pi = 72\pi\) cm\(^2\). [1]
- Curved surface: \(2 \times \pi \times 6 \times 14 = 168\pi\) cm\(^2\). [1]
- Total: \(72\pi + 168\pi = 240\pi = 753.982...\), so the surface area is \(754\) cm\(^2\) correct to 3 significant figures. [1]
The word "closed" is doing real work in this question. An open drum, such as a bucket, would have only one circular end, giving \(36\pi + 168\pi = 204\pi\). Adding the ends is also the step most often forgotten, leaving only the curved surface.
Collecting the terms as multiples of \(\pi\) and rounding only once at the end keeps the third significant figure reliable.
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