Question

Marissa claims that stacking 6 blocks with dimensions of will give the same volume as stacking 9 blocks with dimensions of . Which statements about her claim are true? Check all that apply. Six of the one-half cubes would have a volume of 3 cubic units. Nine of the one-third cubes would have a volume of 6 cubic units. Since and do not have common factors, stacks of one-half cubes and stacks of third-cubes could never have the same volume. Three of the one-third cubes will make 1 unit cube. Two of the one-half cubes will make 1 unit cube. Both stacks will have a volume of 3 cubic units.

Answer 1

a,d,e,f

Step-by-step explanation:

Answer 2

Correction To the Question

• The dimensions of the 6 blocks stacked are
  `(1)/(2)X1X1`
• The dimensions of the 9 blocks stacked are
  `(1)/(3)X1X1`.

Answer:

• (A)Six of the one-half cubes would have a volume of 3 cubic units.
• (D)Three of the one-third cubes will make 1 unit cube.

• (E)Two of the one-half cubes will make 1 unit cube.
• (F)Both stacks will have a volume of 3 cubic units.

Step-by-step explanation:

Marissa claims that stacking 6 blocks with dimensions of
`(1)/(2)X1X1` will give the same volume as stacking 9 blocks with dimensions of
`(1)/(3)X1X1`.

First, we examine the volume of each block.

Block 1

The dimensions are:
`(1)/(2)X1X1`

Volume of 1 block =
`(1)/(2)X1X1=(1)/(2) \:cubic\:units`

Volume of 6 blocks of dimension
`=6 X (1)/(2) =3 \:cubic\:units`

Block 2

The dimensions are:
`(1)/(3)X1X1`

Volume of 1 block =
`(1)/(3)X1X1=(1)/(3) \:cubic\:units`

Volume of 9 blocks of dimension
`=9 X (1)/(3) =3 \:cubic\:units`

The following statements out of her claim are true:

• (A)Six of the one-half cubes would have a volume of 3 cubic units.
• (D)Three of the one-third cubes will make 1 unit cube.
• 
  `3X(1)/(3) =1\:cubic\:unit`
• (E)Two of the one-half cubes will make 1 unit cube.
• 
  `2X(1)/(2) =1\:cubic\:unit`
• (F)Both stacks will have a volume of 3 cubic units.