Difference between revisions of "2003 AMC 10A Problems/Problem 3"

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== Problem ==
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#REDIRECT[[2003 AMC 12A Problems/Problem 3]]
A solid [[rectangular prism|box]] is <math>15</math> cm by <math>10</math> cm by <math>8</math> cm. A new solid is formed by removing a [[cube]] <math>3</math> cm on a side from each corner of this box. What [[percent]] of the original volume is removed?
 
 
 
<math> \mathrm{(A) \ } 4.5\qquad \mathrm{(B) \ } 9\qquad \mathrm{(C) \ } 12\qquad \mathrm{(D) \ } 18\qquad \mathrm{(E) \ } 24 </math>
 
 
 
== Solution ==
 
The volume of the original box is <math>15cm\cdot10cm\cdot8cm=1200cm^{3}</math>
 
 
 
The volume of each cube that is removed is <math>3cm\cdot3cm\cdot3cm=27cm^{3}</math>
 
 
 
Since there are <math>8</math> corners on the box, <math>8</math> cubes are removed.
 
 
 
So the total volume removed is <math>8\cdot27cm^{3}=216cm^{3}</math>.
 
 
 
Therefore, the desired percentage is <math>\frac{216}{1200}\cdot100 = 18\% \rightarrow D</math>.
 
 
 
== See also ==
 
{{AMC10 box|year=2003|ab=A|num-b=2|num-a=4}}
 
 
 
[[Category:Introductory Geometry Problems]]
 

Latest revision as of 16:08, 29 July 2011

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