2020 AMC 10B Problem 2

Below is the professionally curated solution for Problem 2 of the 2020 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 10B solutions, or check the answer key.

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Concepts:volume cube geometry

Difficulty rating: 560

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 the $10$ cubes?

$24$

$25$

$28$

$40$

$45$

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 .

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