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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Another tank Z has its height as 20% more than that of tank R and radius as 20% more than that of tank P. What is the sum of curved surface area of tank P and Z together (approximately)?

  1. A.

    9375 m2

  2. B.

    11548 m2

  3. C.

    8935 m2

  4. D.

    7365 m2

  5. E.

    10296 m2

Show answer & explanation

Correct answer: E

Concept

For a right circular cylinder of radius r and height h, the curved (lateral) surface area is CSA = 2πrh, while the volume is V = πr²h. These are different quantities: CSA grows linearly with radius, volume grows with its square. When a dimension is increased by 20%, the new value is the old value multiplied by 1.2.

Application

  1. Find the base dimensions of tank P. Its volume is given as 38808 m³ with height 28 m. From V = πr²h: r² = 38808 ÷ ((22/7)·28) = 38808 ÷ 88 = 441, so rP = 21 m, hP = 28 m.

  2. Find the dimensions of tank R. Its volume is 5390 m³ with height 35 m. r² = 5390 ÷ ((22/7)·35) = 5390 ÷ 110 = 49, so rR = 7 m, hR = 35 m.

  3. Build tank Z. Its height is 20% more than R's height: hZ = 35 × 1.2 = 42 m. Its radius is 20% more than P's radius: rZ = 21 × 1.2 = 25.2 m ≈ 25 m.

  4. Curved surface area of P: 2πrP·hP = 2 × (22/7) × 21 × 28 = 3696 m².

  5. Curved surface area of Z: 2πrZ·hZ = 2 × (22/7) × 25 × 42 = 6600 m².

  6. Add them: 3696 + 6600 = 10296 m².

Cross-check

Verify the radii against the table: with rP = 21, hP = 28, π = 22/7, the volume πr²h = (22/7)·441·28 = 38808 m³, matching tank P exactly; for R, (22/7)·49·35 = 5390 m³, matching tank R. Note the answer is a surface area (m²), so the option values represent square metres. Using the unrounded rZ = 25.2 gives 3696 + 6652.8 ≈ 10349, and the standard rounding rZ ≈ 25 gives 10296; hence the 'approximately' phrasing, and 10296 is the intended value.

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