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Tank A is a cube that holds 64,000 litres when full. Tank B is also a cube, with each edge twice as long as Tank A's, as shown. How many litres does Tank B hold? litres)

Class 8Cubes and Cube RootsCubes and Roots
  • A128,000 litres
  • B512,000 litres
  • C256,000 litres
  • D4,096,000 litres

Step-by-Step Solution

Tank A: L , so its edge is m. Tank B's edge is 8 m: litres.
Answer: B) 512,000 litres

Key idea: Cube root of negative integers

Cube roots of negatives are real numbers (unlike square roots).

∛ = −∛.

Example: ∛(−125). . So ∛.

This is one place where square root and cube root behave differently — square roots of negatives are NOT real (they're imaginary, a Class 11 topic). Cube roots of negatives are perfectly normal.

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