Volume and Properties of Prisms

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 height and volume, and provides exercises to practice these concepts. Expressions for volume are also discussed, emphasizing the use of commutative and associative properties.

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

• 64/27 cm³

• 81/16 cm³

• 729/64 cm³

• 100/64 cm³

How do you convert 2 and 1/4 to an improper fraction?

• 5/2

• 9/4

• 11/4

• 7/3

What is the volume of a rectangular prism with a base area of 7/12 ft² and a height of 1/3 ft?

• 5/18 ft³

• 7/36 ft³

• 1/4 ft³

• 2/9 ft³

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

• It triples

• It doubles

• It halves

• It remains the same

What is the relationship between height and volume in a rectangular prism?

• Exponentially related

• No relationship

• Inversely proportional

• Directly proportional

How does the volume of a cube change if all side lengths are halved?

• It becomes 1/4 of the original

• It becomes 1/8 of the original

• It doubles

• It remains the same

What happens to the volume of a cube if the side lengths are reduced to one-third?

• It doubles

• It becomes 1/27 of the original

• It remains the same

• It becomes 1/9 of the original

How is the volume of a rectangular prism expressed in terms of base area and height?

• Base area - height

• Base area ÷ height

• Base area + height

• Base area × height

What property allows you to rearrange factors in multiplication?

• Commutative property

• Associative property

• Identity property

• Distributive property

If a cube's side length is divided by 3, what fraction of the original volume does it become?

• 1/27

• 1/9

• 1/3

• 1/81