The transportation cost charged by a shipping company is proportional to the square root of the distance and proportional to the volume of the parcel. If the distance is increased to 4 times, how much volume of the parcel can be transported with the same cost?

Based on the given conditions, the transportation cost (C) can be expressed by the following relationship:

C = k × √D × V

Where k is a constant of proportionality, D is the distance, and V is the volume of the parcel. Let the initial distance and volume be D₁ and V₁. If the distance is increased to four times (D₂ = 4D₁) and the cost remains constant (C₁ = C₂), we set up the equality:

k × √D₁ × V₁ = k × √(4D₁) × V₂

Dividing both sides by k and simplifying the square root (√4 = 2):

√D₁ × V₁ = 2 × √D₁ × V₂

V₁ = 2 × V₂

V₂ = V₁ / 2

Therefore, the new volume V₂ is 0.5 or 50% of the original volume V₁.