This lesson covers the calculation of volume for cubes and rectangular prisms, focusing on using fractional side lengths and base areas. It explores the proportional relationship between changes in dimensions and volume, and provides exercises to reinforce these concepts. Expressions for volume are also discussed, emphasizing the use of variables to represent dimensions.

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

• 729/64 cm³

• 81/16 cm³

• 11 25/64 cm³

• 64/729 cm³

How do you calculate the volume of a rectangular prism with a base area of 7/12 ft² and a height of 1/3 ft?

• Add the base area and height

• Multiply the base area by the height

• Divide the base area by the height

• Subtract the height from the base area

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

• The volume is halved

• The volume remains the same

• The volume is doubled

• The volume is tripled

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

• The volume is halved

• The volume remains the same

• The volume is doubled

• The volume is tripled

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

• The volume is halved

• The volume is doubled

• The volume remains the same

• The volume is reduced to one-eighth

How does the volume of a cube change if all side lengths are reduced to one-fourth?

• The volume is reduced to one-sixty-fourth

• The volume is reduced to one-sixteenth

• The volume remains the same

• The volume is reduced to one-eighth

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

• 36 ft³

• 18 ft³

• 27 ft³

• 54 ft³

If all side lengths of a rectangular prism are halved, what happens to its volume?

• The volume is halved

• The volume is reduced to one-eighth

• The volume is doubled

• The volume remains the same

What is the new volume of a rectangular prism if all side lengths are reduced to one-third?

• The volume remains the same

• The volume is reduced to one-third

• The volume is reduced to one-ninth

• The volume is reduced to one-twenty-seventh

How does changing all side lengths of a shape by the same fractional amount affect its volume?

• The volume remains the same

• The volume changes by the cube of the fractional amount

• The volume changes by the square of the fractional amount

• The volume changes by the fractional amount