Volume of Cubes and Prisms

In lesson 13, Mr. Hul explains the formulas for calculating the volume of cubes and rectangular prisms. The lesson includes examples of calculating volume with whole and fractional side lengths, exercises to practice these calculations, and discussions on writing expressions and using mathematical properties. The lesson concludes with a problem set for further practice.

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

• Length x Width x Height

• Length x Width

• Length + Width + Height

• 2 x (Length + Width + Height)

If a cube has a side length of 9 cm, what is its volume?

• 81 cm³

• 27 cm³

• 729 cm³

• 243 cm³

How do you calculate the volume of a rectangular prism?

• Base Area x Height

• Length x Width

• Length x Width x Height

• Base Area + Height

What happens to the volume of a rectangular prism if its height is doubled?

• The volume is tripled

• The volume remains the same

• The volume is halved

• The volume is doubled

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

• The volume is tripled

• The volume remains the same

• The volume is doubled

• The volume is quadrupled

What is the effect on the volume of a cube if its side lengths are halved?

• The volume is doubled

• The volume remains the same

• The volume is reduced to one-eighth

• The volume is halved

If the side lengths of a cube are reduced to one-fourth, what is the new volume?

• 1/4 of the original volume

• 1/64 of the original volume

• 1/16 of the original volume

• 1/8 of the original volume

How is the volume of a cube expressed in terms of its side length 'e'?

• e²

• e/3

• e³

• 3e

What expression represents the volume of a cube if its side length is divided by 3?

• e³/27

• 3e³

• e³/9

• e³/3

What is the relationship between side length changes and volume in cubes and rectangular prisms?

• Volume changes at the square of the rate of side length changes

• Volume changes at the cube of the rate of side length changes

• Volume changes at the same rate as side length changes

• Volume changes are independent of side length changes