Surface Area Volume and Changing Dimensions

One fish aquarium measures 16 inches long, 5 inches wide, and 10 inches in depth. If another aquarium is the same size except its length is 8 inches long, what is the volume of the smaller fish aquarium?

• 800 in³

• 31 in³

• 400 in³

• 1600 in³

If the length, width, or height of a rectangular prism triples, then the volume will triple as well.

• True

• False

Rectangular prism A has a volume of 8 in³. Rectangular prism B has a volume of 32 in³. The length and width of both prisms is the same. If the height of the smaller prism is 2 inches, then what is the height of the larger prism?

• 4 inches

• 10 inches

• 6 inches

• 8 inches

If the width of the rectangular prism is doubled, which of the following is true?

• The volume increases by 28.

• The volume is eight times as large.

• The volume is half as large.

• The volume is twice as large.

• 2 cubic feet

• 12 cubic feet

• 18 cubic feet

• 108 cubic feet

The box Darnell has for his friend's birthday gift is too short. He needs it to be twice as tall. If he gets another box that has the same width and length, but the height is 2 times taller, how will the volume of his new box compare to his current box?

• The new box's volume will be 2 times bigger.

• The new box's volume will be 2 times smaller.

• The new box's volume will be 4 cubic units more.

• The new box's volume will be 4 cubic units less.

If the length of a rectangular prism is changed by a factor of 3, which of the following is true?

• The surface area changes by a factor of 3.

• The volume changes by a factor of 3.

• The surface area changes by 3.

• The volume changes by 3.

Which statement is NOT true?

• Doubling the length of a prism will double its volume.

• Multiplying the length of a prism by a scale factor of

  4 will multiply the volume by 4.

• There is a direct relationship between a change in

  the length and a change in the volume.

• Doubling the length of a prism will double its surface

  area.

Two similar cones have a scale factor of 8/27. What is the ratio of their volumes?

• 2/3

• 64/729

• 512/19683

• 8/27

If all of the dimensions of a triangular prism decreased by 1/3, how much would the volume decrease by?

• 1/27

• 1/9

• 1/3

• 1/6