Difference between revisions of "2013 AMC 8 Problems/Problem 18"
Megaboy6679 (talk | contribs) m (→Solution 2) |
(→See Also) |
||
(4 intermediate revisions by 3 users not shown) | |||
Line 1: | Line 1: | ||
==Problem== | ==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? | + | Isabella uses one-foot cubical blocks to build a rectangular fort that is <math>12</math> feet long, <math>10</math> feet wide, and <math>5</math> feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain? |
<asy>import three; | <asy>import three; | ||
Line 68: | Line 68: | ||
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>. | ||
− | 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> | + | 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> |
== Video Solution by OmegaLearn == | == Video Solution by OmegaLearn == |
Latest revision as of 22:30, 18 December 2023
Contents
Problem
Isabella uses one-foot cubical blocks to build a rectangular fort that is feet long,
feet wide, and
feet high. The floor and the four walls are all one foot thick. How many blocks does the fort contain?
Solution 1
There are 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
cubes. Hence, the answer is
.
Solution 2 (Complementary Counting)
We can just calculate the volume of the prism that was cut out of the original box. Each interior side of the fort will be
feet shorter than each side of the outside. Since the floor is
foot, the height will be
feet. So the volume of the interior box is
.
The volume of the original box is . Therefore, the number of blocks contained in the fort is
Video Solution by OmegaLearn
https://youtu.be/FDgcLW4frg8?t=5261
~ pi_is_3.14
Video Solution 2
https://youtu.be/WlMUXUloTFM Soo, DRMS, NM
Video Solution 3
https://youtu.be/zFNf8WxBdoY ~savannahsolver
See Also
(Other problems)
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.