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

Correction To the Question

• The dimensions of the 6 blocks stacked are $\frac{1}{2}X1X1$
• The dimensions of the 9 blocks stacked are $\frac{1}{3}X1X1$.

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.

Explanation:

Marissa claims that stacking 6 blocks with dimensions of $\frac{1}{2}X1X1$ will give the same volume as stacking 9 blocks with dimensions of $\frac{1}{3}X1X1$.

First, we examine the volume of each block.

Block 1

The dimensions are: $\frac{1}{2}X1X1$

Volume of 1 block =$\frac{1}{2}X1X1=\frac{1}{2} \:cubic\:units$

Volume of 6 blocks of dimension $=6 X \frac{1}{2} =3 \:cubic\:units$

Block 2

The dimensions are: $\frac{1}{3}X1X1$

Volume of 1 block =$\frac{1}{3}X1X1=\frac{1}{3} \:cubic\:units$

Volume of 9 blocks of dimension $=9 X \frac{1}{3} =3 \:cubic\:units$

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.
• $3X\frac{1}{3} =1\:cubic\:unit$
• (E)Two of the one-half cubes will make 1 unit cube.
• $2X\frac{1}{2} =1\:cubic\:unit$
• (F)Both stacks will have a volume of 3 cubic units.