Difference between revisions of "2018 AMC 10B Problems/Problem 10"
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==Solution== | ==Solution== | ||
| − | Consider the cross-sectional plane. Note that <math>bh/2=3</math> and we want <math>bh/3</math>, so the answer is <math>2</math> | + | Consider the cross-sectional plane. Note that <math>bh/2=3</math> and we want <math>bh/3</math>, so the answer is <math>2</math> (AOPS12142015) |
Revision as of 14:54, 16 February 2018
In the rectangular parallelpiped shown, 
= 
, 
= 
, and 
= 
. Point 
is the midpoint of 
. What is the volume of the rectangular pyramid with base 
and apex ?
![[asy] size(250); defaultpen(fontsize(10pt)); pair A =origin; pair B = (4.75,0); pair E1=(0,3); pair F = (4.75,3); pair G = (5.95,4.2); pair C = (5.95,1.2); pair D = (1.2,1.2); pair H= (1.2,4.2); pair M = ((4.75+5.95)/2,3.6); draw(E1--M--H--E1--A--B--E1--F--B--M--C--G--H); draw(B--C); draw(F--G); draw(A--D--H--C--D,dashed); label("$A$",A,SW); label("$B$",B,SE); label("$C$",C,E); label("$D$",D,W); label("$E$",E1,W); label("$F$",F,SW); label("$G$",G,NE); label("$H$",H,NW); label("$M$",M,N); dot(A); dot(B); dot(E1); dot(F); dot(G); dot(C); dot(D); dot(H); dot(M);[/asy]](http://latex.artofproblemsolving.com/d/c/6/dc6049797801ea50f14860fa92c1464b9ae29320.png)
Solution
Consider the cross-sectional plane. Note that 
and we want 
, so the answer is (AOPS12142015)
