Question
what's the volume of a rectangular prism with 2/3,7/8, and 1/3 cm
Answers
GPT-4o mini
To find the volume of a rectangular prism, you multiply its length, width, and height. Given the dimensions \( \frac{2}{3} \) cm, \( \frac{7}{8} \) cm, and \( \frac{1}{3} \) cm, the volume \( V \) can be calculated as follows:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
\[
V = \frac{2}{3} \times \frac{7}{8} \times \frac{1}{3}
\]
To multiply these fractions, multiply the numerators together and the denominators together:
\[
V = \frac{2 \times 7 \times 1}{3 \times 8 \times 3}
\]
Calculating the numerator and denominator:
- Numerator: \( 2 \times 7 \times 1 = 14 \)
- Denominator: \( 3 \times 8 \times 3 = 72 \)
So, we have:
\[
V = \frac{14}{72}
\]
Next, simplify the fraction. Both 14 and 72 can be divided by 2:
\[
V = \frac{7}{36}
\]
Therefore, the volume of the rectangular prism is \( \frac{7}{36} \) cubic centimeters.
\[
V = \text{length} \times \text{width} \times \text{height}
\]
\[
V = \frac{2}{3} \times \frac{7}{8} \times \frac{1}{3}
\]
To multiply these fractions, multiply the numerators together and the denominators together:
\[
V = \frac{2 \times 7 \times 1}{3 \times 8 \times 3}
\]
Calculating the numerator and denominator:
- Numerator: \( 2 \times 7 \times 1 = 14 \)
- Denominator: \( 3 \times 8 \times 3 = 72 \)
So, we have:
\[
V = \frac{14}{72}
\]
Next, simplify the fraction. Both 14 and 72 can be divided by 2:
\[
V = \frac{7}{36}
\]
Therefore, the volume of the rectangular prism is \( \frac{7}{36} \) cubic centimeters.