2020 AMC 10B Problem 2

Problem 2 of 25EasierGeometry

Carl has

5

cubes each having side length

1,

and Kate has

5

cubes each having side length

2.

What is the total volume of these

10

cubes?

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Solution

A cube with side length

s

has volume

s^3.

Carl’s five cubes have total volume

5\cdot 1^3=5,

and Kate’s five cubes have total volume

5\cdot 2^3=40.

The total volume is

5+40=45.

Thus, the correct answer is E .

Concepts: volume · cube geometry

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.