Volume of Prisms and Cubes

The video tutorial covers lesson 13 on volume formulas, focusing on calculating the volume of cubes and rectangular prisms using fractional side lengths. It includes examples, exercises, and explores the relationship between height and volume. The tutorial also demonstrates how to use expressions and mathematical properties to understand volume changes, and provides instructions for exercises on page 76.

What is the volume of a cube with side lengths of 2 1/4 cm?

• 64 cm³

• 729 cm³

• 81/16 cm³

• 729/64 cm³

How do you calculate the volume of a rectangular prism if you know the base area and height?

• Subtract the height from the base area

• Add the base area and height

• Multiply the base area by the height

• Divide the base area by the height

If the height of a prism is doubled, what happens to its volume?

• The volume is tripled

• The volume is halved

• The volume is doubled

• The volume remains the same

What happens to the volume of a cube if each side length is halved?

• The volume remains the same

• The volume is doubled

• The volume is reduced to one-eighth

• The volume is halved

How is the volume of a cube affected if the side lengths are reduced to one-fourth of their original length?

• The volume remains unchanged

• The volume is reduced to one-sixty-fourth

• The volume is reduced to one-sixteenth

• The volume is reduced to one-fourth

What is the volume of a rectangular prism with dimensions 9 ft, 2 ft, and 3 ft?

• 27 ft³

• 54 ft³

• 36 ft³

• 18 ft³

If the side lengths of a rectangular prism are halved, what is the new volume compared to the original?

• One-fourth of the original volume

• One-eighth of the original volume

• One-sixteenth of the original volume

• One-half of the original volume

What expression represents the volume of a cube with side length 'e'?

• e/3

• e²

• e³

• 3e

How do you express the volume of a cube if the side length is divided by 3?

• e³/27

• 3e³

• e³/9

• e³/3

If the height of a rectangular prism is quadrupled, what happens to its volume?

• The volume remains the same

• The volume is doubled

• The volume is quadrupled

• The volume is halved