# 2020 AMC 10B Problems/Problem 2

## Problem

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? $\textbf{(A)}\ 24 \qquad\textbf{(B)}\ 25 \qquad\textbf{(C)}\ 28 \qquad\textbf{(D)}\ 40 \qquad\textbf{(E)}\ 45$

## Solution 1

A cube with side length $1$ has volume $1^3=1$, so $5$ of these will have a total volume of $5\cdot1=5$.

A cube with side length $2$ has volume $2^3=8$, so $5$ of these will have a total volume of $5\cdot8=40$. $5+40=\boxed{\textbf{(E) }45}$ ~quacker88

## Solution 2

The total volume of Carl's cubes is $5$. This is because to find the volume of a cube or a rectangular prism, you have to multiply the height by the length by the width. So in this question, it would be $1 \times 1 \times 1$. This is equal to $1$. Since Carl has 5 cubes, you will have to multiply $1$ by $5$, to account for all the $5$ cubes.

Next, to find the total volume of Kate's cubes you have to do the same thing. Except, this time, the height, the width, and the length, are all $2$, so it will be $2 \times 2 \times 2 = 8.$ Now you have to multiply by $5$ to account for all the $5$ blocks. This is $40$. So the total volume of Kate's cubes is $40$.

Lastly, to find the total of Carl's and Kate's cubes, you must add the total volume of these people. This is going to be $5+40=\boxed{\textbf{(E)} ~45}$.

- BrightPorcupine

~MrThinker

## Video Solution (HOW TO THINK CRITICALLY!!!)

Check It Out! :) ~Education, the study of everything

~savannahsolver

~AlexExplains

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 