2020 AMC 10B Problem 2

Question

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?

24

25

28

40

45

A cube with side length

s

has volume

s^3

Find the volume from Carl’s cubes and Kate’s cubes separately

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 .

Problem 2 in other years