Question
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
2 cm, 8 cm, 9 cm
3 cm, 6 cm, 9 cm
3 cm, 3 cm, 9 cm
4 cm, 5 cm, 9 cm
Answers
GPT-4o mini
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**.
\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]
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**.