Building a 3D Object from Its Top, Front and Side Views

0:00These three views show one object made of cubes. What is the object?

0:06Each view looks straight at the object: the top view from above, the front view from the front, and the side view from the right.

0:15The top view shows the footprint: the squares where cubes stand.

0:20Each square holds a stack of at least one cube, so we need to find five heights.

0:26The front view shows the tallest stack in each column, left to right: 3, 1 and 2.

0:33The middle column is only 1 cube tall, so both of its stacks have 1 cube.

0:39The right column has one square, so that stack has 2 cubes.

0:45The side view shows the tallest stack in each row, front to back: 2 and 3.

0:51A common mistake: skip the side view and guess the left column's 3 is at the front.

0:58Then the front row would be 3 tall, but the side view says 2, so the 3 is at the back.

1:05The front left stack has 1 or 2 cubes, since the front row only reaches 2. Try 1.

1:12Check: from the front, the columns are 3, 1 and 2, and from the side, the rows are 2 and 3.

1:20In all, 1 plus 1 plus 2 plus 3 plus 1 makes 8 cubes.

1:27Now copy it and add a second cube to the front left stack.

1:32The left column is still 3 and the front row is still 2, so no view changes.

1:38Two different objects, with 8 and 9 cubes, have the same three views.

1:44The top view gives the footprint, and the front and side views give the tallest stacks.