Which could be the length, width, and height of a rectangular prism with a volume of 81 cm 3?

2 cm, 8 cm, 9 cm

3 cm, 6 cm, 9 cm

3 cm, 3 cm, 9 cm

4 cm, 5 cm, 9 cm

1 answer

To find the possible dimensions of a rectangular prism with a volume of 81 cm³, we can use the formula for the volume of a rectangular prism, which is given by:

\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]

We need to check which sets of dimensions multiply to 81 cm³.

  1. 2 cm, 8 cm, 9 cm \[ 2 \times 8 \times 9 = 144 , \text{cm}^3 \]

  2. 3 cm, 6 cm, 9 cm \[ 3 \times 6 \times 9 = 162 , \text{cm}^3 \]

  3. 3 cm, 3 cm, 9 cm \[ 3 \times 3 \times 9 = 81 , \text{cm}^3 \]

  4. 4 cm, 5 cm, 9 cm \[ 4 \times 5 \times 9 = 180 , \text{cm}^3 \]

The only combination that results in a volume of 81 cm³ is:

3 cm, 3 cm, 9 cm.