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alisha [4.7K]
2 years ago
9

Marissa claims that stacking 6 blocks with dimensions of will give the same volume as stacking 9 blocks with dimensions of . Whi

ch 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.
English
1 answer:
Marta_Voda [28]2 years ago
5 0

<u>Correction To the Question</u>

  • 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.

<u>Block 1</u>

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

<u>Block 2</u>

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.

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