Difference between revisions of "2025 AMC 8 Problems/Problem 8"

Revision as of 21:08, 29 January 2025

Problem

Isaiah cuts open a cardboard cube along some of its edges to form the flat shape shown on the right, which has an area of 18 square centimeters. What is the volume of the cube in cubic centimeters?

$\textbf{(A)}~3\sqrt{3}\qquad\textbf{(B)}~6\qquad\textbf{(C)}~9\qquad\textbf{(D)}~6\sqrt{3}\qquad\textbf{(E)}~9\sqrt{3}$

Solution

Observe that since the six squares on the net are congruent, each of them has area $\frac{18}{6}=3$ . Hence, the side length of the cube is $\sqrt{3}$ . Its volume is then $(\sqrt{3})^3=\boxed{\textbf{(A)}~3\sqrt{3}}$ . ~cxsmi

@@ Line 1: / Line 1: @@
-The 2025 AMC 8 is not held yet. Please do not post false problems.
+==Problem==
+Isaiah cuts open a cardboard cube along some of its edges to form the flat shape shown on the right, which has an area of 18 square centimeters. What is the volume of the cube in cubic centimeters?
+<math>\textbf{(A)}~3\sqrt{3}\qquad\textbf{(B)}~6\qquad\textbf{(C)}~9\qquad\textbf{(D)}~6\sqrt{3}\qquad\textbf{(E)}~9\sqrt{3}</math>
+==Solution==
+Observe that since the six squares on the net are congruent, each of them has area <math>\frac{18}{6}=3</math>. Hence, the side length of the cube is <math>\sqrt{3}</math>. Its volume is then <math>(\sqrt{3})^3=\boxed{\textbf{(A)}~3\sqrt{3}}</math>. ~cxsmi

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Difference between revisions of "2025 AMC 8 Problems/Problem 8"

Revision as of 21:08, 29 January 2025

Problem

Solution