AMC 8 Daily Practice Round 7

Complete problem set with solutions and individual problem pages

Problem 16 Easy

As shown in the figure below, three cubes with edge lengths of 1cm, 2cm, and 3cm are attached closely together. What is the surface area of the resulting three-dimensional figure in square centimeters?

  • A.

    74

  • B.

    77

  • C.

    80

  • D.

    83

  • E.

    84

Answer:A

Through observation, we find that when the three cubes are attached closely together, some surfaces are covered:

the bottom surface of cube A, part of the top and bottom surfaces of cube B, and part of the top surface of cube C.

The total surface area is calculated as follows: 6 \times 1^2 + 6 \times 2^2 + 6 \times 3^2 - 2 \times 1^2 - 2 \times 2^2 = 74 cm^{2}.

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