Difference between revisions of "2018 AMC 10B Problems/Problem 10"
Ishankhare (talk | contribs) (Created page with "In the rectangular parallelpiped shown, <math>AB</math> = 3, <math>BC</math> = 1, and <math>CG</math> = 2. Point <math>M</math> is the midpoint of <math>\overline{FG}</math>....") |
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| Line 2: | Line 2: | ||
| − | + | <asy> | |
size(250); | size(250); | ||
| Line 19: | Line 19: | ||
draw(F--G); | draw(F--G); | ||
draw(A--D--H--C--D,dashed); | draw(A--D--H--C--D,dashed); | ||
| − | label(" | + | label("$A$",A,SW); |
| − | label(" | + | label("$B$",B,SE); |
| − | label(" | + | label("$C$",C,E); |
| − | label(" | + | label("$D$",D,W); |
| − | label(" | + | label("$E$",E1,W); |
| − | label(" | + | label("$F$",F,SW); |
| − | label(" | + | label("$G$",G,NE); |
| − | label(" | + | label("$H$",H,NW); |
| − | label(" | + | label("$M$",M,N); |
dot(A); | dot(A); | ||
dot(B); | dot(B); | ||
| Line 36: | Line 36: | ||
dot(D); | dot(D); | ||
dot(H); | dot(H); | ||
| − | dot(M); | + | dot(M);</asy> |
<math>\textbf{(A) } 1 \qquad \textbf{(B) } \frac{4}{3} \qquad \textbf{(C) } \frac{3}{2} \qquad \textbf{(D) } \frac{5}{3} \qquad \textbf{(E) } 2</math> | <math>\textbf{(A) } 1 \qquad \textbf{(B) } \frac{4}{3} \qquad \textbf{(C) } \frac{3}{2} \qquad \textbf{(D) } \frac{5}{3} \qquad \textbf{(E) } 2</math> | ||
Revision as of 14:31, 16 February 2018
In the rectangular parallelpiped shown, 
= 3, 
= 1, and 
= 2. 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)
