AMC 8 Daily Practice Round 7

Complete problem set with solutions and individual problem pages

Problem 20 Easy

There is a cube wooden block with an edge length of 5cm. There are penetrating holes (shown as black parts in the figure) when viewed from the front and the right side. What is the volume of this three-dimensional figure in cubic centimeters?

  • A.

    54

  • B.

    56

  • C.

    62

  • D.

    68

  • E.

    74

Answer:D

We can calculate the volume by dividing the cube into five layers from top to bottom:

The first and fifth layers have no holes, and the volume of each layer is 5 \times 5 \times 1 = 25 cubic centimeters.

The volume of the second layer is 10 \times 1 = 10 cubic centimeters.

The volume of the third layer is 4 \times 1 = 4 cubic centimeters.

The volume of the fourth layer is 4 \times 1 = 4 cubic centimeters.

Adding them up, the total volume is: 25 + 25 + 10 + 4 + 4 = 68 cubic centimeters.

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