Volume and Packing of Prisms

This lesson covers the concept of volume with fractional edge lengths, focusing on calculating the volume of prisms using base area and height. Examples include using half-inch and quarter-inch cubes to fill prisms, and exercises involve calculating the volume of rectangular prisms. A practical problem of packing toy boxes into a larger box is also discussed. The lesson concludes with a comparison of cubes with different side lengths and a problem set for practice.

What is the formula for calculating the volume of a prism?

• Length x Width x Height

• Base Area x Width

• Base Area x Height

• Length x Width

How many more unit cubes does the larger prism hold compared to the smaller one?

• 240

• 480

• 120

• 360

If a cube is cut in half, how many smaller cubes are needed to fill the original cube?

• 2

• 4

• 8

• 6

How many quarter-inch cubes are needed to fill a one-inch cube?

• 64

• 128

• 16

• 32

What is the volume of a prism with a base area of 32/9 cm² and a height of 4/3 cm?

• 16/3 cm³

• 32/9 cm³

• 64/9 cm³

• 128/27 cm³

How many 1/3 inch cubes fit into a prism with a volume of 128/27 cm³?

• 512

• 256

• 128

• 64

What is the greatest number of small toy boxes that can be packed into a larger box with dimensions 12 in x 4.5 in x 3.5 in?

• 1512

• 2160

• 1890

• 2016

Why does it take more 1/3 unit cubes than 1/2 unit cubes to fill the same volume?

• 1/2 unit cubes are smaller

• 1/2 unit cubes are larger

• 1/3 unit cubes are smaller

• 1/3 unit cubes are larger

What is the volume of a rectangular prism with dimensions 5 1/3 cm x 2/3 cm x 1 1/3 cm?

• 7 1/2 cm³

• 5 1/6 cm³

• 6 1/3 cm³

• 4 20/27 cm³

How many 1/3 inch cubes are needed to fill a prism with a volume of 8 cubic units?

• 512

• 216

• 128

• 64