Arun makes a popular brand of ice cream in a rectangular shaped bar 6cm long,…

2026

Arun makes a popular brand of ice cream in a rectangular shaped bar 6cm long, 5cm wide and 2cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain same, but the length and width will be decreased by some percentage. The new width will be ___

  1. A.

    5.5

  2. B.

    4.5

  3. C.

    7.5

  4. D.

    6.5

Attempted by 1 students.

Show answer & explanation

Correct answer: B

Concept

For a cuboid, Volume = Length × Width × Thickness. When the thickness stays fixed, the volume is directly proportional to the base area (Length × Width). If two dimensions are each scaled down by the SAME linear factor r, the base area scales by r2 — not by r itself — so an area ratio must be square-rooted to get back the linear scale factor.

Working

  1. Original volume = 6 × 5 × 2 = 60 cm3.

  2. A 19% cut leaves 81% of the volume: 60 × 0.81 = 48.6 cm3.

  3. Thickness is unchanged at 2 cm, so the new base area = 48.6 ÷ 2 = 24.3 cm2.

  4. Original base area = 6 × 5 = 30 cm2; ratio of new area to old area = 24.3 ÷ 30 = 0.81.

  5. Length and width shrink by the same linear factor r, so the area ratio is r2 = 0.81, giving r = √0.81 = 0.9.

  6. New width = original width × r = 5 × 0.9 = 4.5 cm.

Cross-check

New length = 6 × 0.9 = 5.4 cm. Recomputed volume = 5.4 × 4.5 × 2 = 48.6 cm3, which matches the required 81% of the original 60 cm3 — confirming the new width.

Reference figure

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