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10-6.

     Paul built a tower by stacking six identical layers of the shape at right on top of each other. 

  1. What is the volume of his tower? How can you tell without building the shape?

  2. What is the surface area of his tower?

  3. Paul’s tower is an example of a prism (refer to the Math Notes box in this lesson to learn more about prisms). For each of the prisms below, determine the volume and surface area.

A tower with numerous layers of cubes on a 3 x 3 grid. The layer is composed of a column of 3 cubes at the left side, two cubes in the middle second and third rows, and two cubes at the right in the first and second rows.

 1. A tower of 5 layers of cubes.  Each layer is built with 4 cubes. The first column has two cubes in the second and third rows. The second column has 2 cubes in the first and second rows.

Remember the volume of a prism is (area of the base) · (height).

 2. A tower of 4 layers of cubes.  Each layer is built with 6 cubes. The first column has 3 cubes one in each row. The second columns has 2 cubes in the second and third rows. The third column has 1 cube in the third row.

The total surface area of a prism is the area of all of the external faces of the prism.

Try separating the calculations into: surface area of the base/top + surface area of the sides.

 3.  A rectangular prism with a length of 4, a width of 3, and a height of 5.

Tower (1):
V units, SA units