Difference between revisions of "2020 AMC 10B Problems/Problem 2"
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==Problem== | ==Problem== | ||
− | What is the | + | Carl has <math>5</math> cubes each having side length <math>1</math>, and Kate has <math>5</math> cubes each having side length <math>2</math>. What is the total volume of these <math>10</math> cubes? |
− | < | ||
− | <math>\textbf{(A)}\ | + | <math>\textbf{(A)}\ 24 \qquad\textbf{(B)}\ 25 \qquad\textbf{(C)}\ 28 \qquad\textbf{(D)}\ 40 \qquad\textbf{(E)}\ 45</math> |
==Solution== | ==Solution== | ||
− | A cube with side length <math>1</math> has volume <math>1^3=1</math> | + | A cube with side length <math>1</math> has volume <math>1^3=1</math>, so <math>5</math> of these will have a total volume of <math>5\cdot1=5</math>. |
− | A cube with side length <math>2</math> has volume <math>2^3=8</math> | + | A cube with side length <math>2</math> has volume <math>2^3=8</math>, so <math>5</math> of these will have a total volume of <math>5\cdot8=40</math>. |
− | <math>5+40=\boxed{\textbf{(E) } | + | <math>5+40=\boxed{\textbf{(E) }45}</math> ~quacker88 |
+ | |||
+ | ==Video Solution== | ||
+ | https://youtu.be/Gkm5rU5MlOU | ||
+ | |||
+ | ~IceMatrix | ||
+ | |||
+ | https://youtu.be/FcPO4EXDwzc | ||
+ | |||
+ | ~savannahsolver | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{AMC10 box|year=2020|ab=B|num-b=1|num-a=3}} | ||
+ | {{MAA Notice}} |
Revision as of 16:59, 16 June 2020
Contents
Problem
Carl has cubes each having side length , and Kate has cubes each having side length . What is the total volume of these cubes?
Solution
A cube with side length has volume , so of these will have a total volume of .
A cube with side length has volume , so of these will have a total volume of .
~quacker88
Video Solution
~IceMatrix
~savannahsolver
See Also
2020 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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