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The table below shows data about four cylindrical tanks P, Q, R and S, including their volume, height, and time taken by inlet pipe A, inlet pipe B, and outlet pipe C to fill or empty the tank. 1. The ratio between the time taken by pipe B and the time taken by pipe C is different because different methods of pipe usage are used by the operator for different tanks. 2. The radius of tank S is 10.5 meters. Tank | Volume (m³) | Height (m) | Time taken (in hours) | Ratio of time taken by pipe B to time taken by pipe C P | 38808 | 28 | 10 | 2:3 Q | — | 10 | 12 | 3:2 R | 5390 | 35 | 18 | 1:3 S | 19250 | — | — | 2:5 Find the ratio of the curved surface area of tank P to the total surface area of tank R.

1. 2:3
2. 4:3
3. 2:1
4. 3:1

Correct answer: 2:1

Solution

For tank P, \(V=\pi r^2 h\), so \(38808=\pi r^2 \cdot 28\), giving \(r=21\) m. Thus CSA of P = \(2\pi rh = 2\pi \cdot 21 \cdot 28\). For tank R, \(5390=\pi r^2 \cdot 35\), giving \(r=7\) m, so TSA of R = \(2\pi r(r+h)=2\pi \cdot 7(7+35)\). The ratio simplifies to 2:1.

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