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.
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2 cm, 8 cm, 9 cm \[ 2 \times 8 \times 9 = 144 , \text{cm}^3 \]
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3 cm, 6 cm, 9 cm \[ 3 \times 6 \times 9 = 162 , \text{cm}^3 \]
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3 cm, 3 cm, 9 cm \[ 3 \times 3 \times 9 = 81 , \text{cm}^3 \]
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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.