Question

Marissa claims that stacking 6 blocks with dimensions of One-half times 1 times 1 will give the same volume as stacking 9 blocks with dimensions of One-third times 1 times 1. 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 One-half and One-third 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. HURRRY OR ILL GET A F :(

Answer 1

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

First, let us examine the volume of each of the blocks.

For 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   $=6* \frac{1}{2} =3 cubic units$

For 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 $=9*\frac{1}{3} =3 cubic units$  

The following statements out of Marissa's 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.

 $3*\frac{1}{3} =1 cubic units$

(E)Two of the one-half cubes will make 1 unit cube.

 $2*\frac{1}{2} =1 cubic units$

(F)Both stacks will have a volume of 3 cubic units.