Problem 327

{{searchResults.length}} results for “{{searchWords}}” No results found for “{{searchWords}}” × back to contents

§{{x[0]}} {{x[1]}}

Table of Contents

Problem 327: (2005 AMC 12a, 17)

A unit cube is cut twice to form three triangular prisms, two of which are congruent, as shown in Figure 1. The cube is then cut in the same manner along the dashed lines shown in Figure 2. This creates nine pieces. What is the volume of the piece that contains vertex $W$? $(\mathrm {A}) \ \frac {1}{12} \qquad (\mathrm {B}) \ \frac {1}{9} \qquad (\mathrm {C})\ \frac {1}{8} \qquad (\mathrm {D}) \ \frac {1}{6} \qquad (\mathrm {E})\ \frac {1}{4}$

Solution

Exercise 327: Solution

A cube $ABCDEFGH$ with edge length $6$ has bottom face $ABCD$ and top face $EFGH$, with $E$ above $A$, $F$ above $B$, $G$ above $C$, and $H$ above $D$. A plane through $A$, $C$, and the midpoint of $\overline{FG}$ cuts the cube into two pieces. What is the volume of the piece that contains vertex $B$?

Search Go to Prev Next

Contact Us