Multiple choice

Find the correct relationship between the given quantities: Quantity I: Value of ‘x’. A cylinder having height 196 cm and radius 14 cm is casted into ‘x’ number of cubes having side 7 cm. Quantity II: Find the height of the cone in cm (approximately).Curved surface area of a right circular cone is 176 m2 and its base diameter is 1400 cm.

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Cylinder volume = π × 14² × 196 = π × 196 × 196 = 38416π cm³. Cube volume = 7³ = 343 cm³. Number of cubes x = 38416π/343 ≈ 112π ≈ 352. Quantity II: Cone diameter = 1400 cm = 14 m, so radius = 7 m. CSA = πrl = 176, so π × 7 × l = 176, giving l = 176/(7π) ≈ 8 m. Height h = √(l² - r²) = √(64 - 49) = √15 ≈ 3.87 m = 387 cm. Quantity II ≈ 387 > Quantity I ≈ 352. Option A is correct.

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