Track / Stage 4 / 249 of 340 #509 of 1964

Problem 509

AMC 12 late, AIME early

Geometry Difficulty 4.9 Multiple choice

In the diagram, the rectangular solid and the cube have equal volumes. The length of each edge of the cube is

Pick one

Official solution

The volume of the rectangular solid is $2 \times 4 \times 8=64$ .

If the length of each edge of the cube is $s$ , then the volume of the cube is $s^{3}$ , which must be equal to 64 . Since $s^{3}=64$ , then $s=4$ , so the length of each edge of the cube is 4 .

ANSWER: (B)

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.