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Difference between revisions of "2013 AMC 8 Problems/Problem 18"

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We can just calculate the volume of the prism that was cut out of the original <math>12\times 10\times 5</math> box. Each interior side of the fort will be <math>2</math> feet shorter than each side of the outside. Since the floor is <math>1</math> foot, the height will be <math>4</math> feet. So the volume of the interior box is <math>10\times 8\times 4=320\text{ ft}^3</math>.
 
We can just calculate the volume of the prism that was cut out of the original <math>12\times 10\times 5</math> box. Each interior side of the fort will be <math>2</math> feet shorter than each side of the outside. Since the floor is <math>1</math> foot, the height will be <math>4</math> feet. So the volume of the interior box is <math>10\times 8\times 4=320\text{ ft}^3</math>.
  
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The volume of the original box is <math>12\times 10\times 5=600\text{ ft}^3</math>. Therefore, the number of block contained in the fort is <math>600-320=\boxed{\textbf{(B)}\ 280}</math>.
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The volume of the original box is <math>12\times 10\times 5=600\text{ ft}^3</math>. Therefore, the number of blocks contained in the fort is <math>600-320=\boxed{\textbf{(B)}\ 280}</math>.
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2013|num-b=17|num-a=19}}
 
{{AMC8 box|year=2013|num-b=17|num-a=19}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 23:43, 27 November 2013

Problem

Isabella uses one-foot cubical blocks to build a rectangular fort that is 12 feet long, 10 feet wide, and 5 feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain?

Box.png

--Arpanliku 16:22, 27 November 2013 (EST) Courtesy of Lord.of.AMC

$\textbf{(A)}\ 204 \qquad \textbf{(B)}\ 280 \qquad \textbf{(C)}\ 320 \qquad \textbf{(D)}\ 340 \qquad \textbf{(E)}\ 600$

Solution 1

There are $10 \cdot 12 = 120$ cubes on the base of the box. Then, for each of the 4 layers above the bottom (as since each cube is 1 foot by 1 foot by 1 foot and the box is 5 feet tall, there are 4 feet left), there are $9 + 11 + 9 + 11 = 40$ cubes. Hence, the answer is $120 + 4 \cdot 40 = \boxed{\textbf{(B)}\ 280}$.

Solution 2

We can just calculate the volume of the prism that was cut out of the original $12\times 10\times 5$ box. Each interior side of the fort will be $2$ feet shorter than each side of the outside. Since the floor is $1$ foot, the height will be $4$ feet. So the volume of the interior box is $10\times 8\times 4=320\text{ ft}^3$.

The volume of the original box is $12\times 10\times 5=600\text{ ft}^3$. Therefore, the number of blocks contained in the fort is $600-320=\boxed{\textbf{(B)}\ 280}$.

See Also

2013 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 17 		Followed by
Problem 19
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 AJHSME/AMC 8 Problems and Solutions

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