Question

A unit cube is shown.

What is the volume of the following figure?
The front view of a figure shows the top and front side. It is four blocks high. Each layer has different color blocks. The fourth (top) layer has 2 pink blocks: 1 row and 2 columns. The third layer has 2 green blocks: 1 row and 2 columns. The second layer has 8 blue blocks: 4 rows and 2 columns. The first (bottom) layer has 8 red blocks: 4 rows and 2 columns.
The back view of the same figure shows the bottom and back side. It is four blocks high. Each layer has different colors. In the first (bottom) layer there are 8 red blocks: 4 rows and 2 columns. The second layer has 8 blue blocks: 4 rows and 2 columns. The third layer has 2 green blocks: 1 row and 2 columns. The fourth (top) layer has 2 pink blocks: 1 row and 2 columns.

Answer 1

Answer: The figure is made up of two parts, the front and the back. Each part has a volume of 8 blocks, so the total volume is 16 blocks.

Alternatively, we can find the volume by adding up the volumes of each layer. The top layer has a volume of 2 blocks, the second and third layers have a volume of 8 blocks each, and the bottom layer has a volume of 8 blocks. So the total volume is 2 + 8 + 8 + 8 = 26 cubic units. However, we need to subtract the volume of the blocks that are hidden from view. The blocks that are hidden in the front view are the two blue blocks in the front of the third layer, and the blocks that are hidden in the back view are the two red blocks in the back of the first layer. So the total volume of the figure is 26 - 2 - 2 = 22 cubic units.

Explanation: