Direction : Read the given below table carefully and answer the following…

2021

Direction : Read the given below table carefully and answer the following questions.
The data shows volume and height of 4 right circular tanks P, Q, R and S. The given data also depicts time taken to fill or empty the tank by inlet pipe A, B and outlet pipe C.
1. Ratio between time taken by pipe B and that by pipe C is different because pipes were used by the operator in different ways for different tanks.
2. Radius of tank S is 10.5 m.

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Find respective ratio of curved surface area of tank P and total surface area of tank R.

  1. A.

    2: 3

  2. B.

    4: 3

  3. C.

    2: 1

  4. D.

    3: 1

  5. E.

    None of these

Show answer & explanation

Correct answer: C

Concept

For a right circular cylinder of radius r and height h: Volume V = πr2h, Curved Surface Area (CSA) = 2πrh, and Total Surface Area (TSA) = 2πr(r + h). To compare surface areas across two cylinders, first recover each unknown radius from its volume and height using the volume formula, then substitute into the required surface-area formula. Use π = 22/7.

Application

  1. Tank P — find the radius. From V = πr2h: 38808 = (22/7) × r2 × 28, so r2 = 38808 × 7 / (22 × 28) = 441, giving r = 21 m.

  2. Tank P — CSA = 2πrh = 2 × (22/7) × 21 × 28 = 3696 m2.

  3. Tank R — find the radius. From V = πr2h: 5390 = (22/7) × r2 × 35, so r2 = 5390 × 7 / (22 × 35) = 49, giving r = 7 m.

  4. Tank R — TSA = 2πr(r + h) = 2 × (22/7) × 7 × (7 + 35) = 2 × 22 × 42 = 1848 m2.

  5. Required ratio = CSA of P : TSA of R = 3696 : 1848 = 2 : 1 (divide both by 1848).

Cross-check

Reduce independently: 3696 / 1848 = 2 exactly, so the ratio is 2 : 1. Note the volume and height columns are the only data needed here; the pipe-time and pipe-ratio columns are not used for a surface-area comparison.

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