To determine the volume of a rectangular prism, we use the formula:
[tex]\[ \text{Volume} = \text{Height} \times \text{Base Area} \][/tex]
In this case, the given height of the rectangular prism is [tex]\( 22 \frac{1}{2} \)[/tex] centimeters, and the base area is [tex]\( 562 \frac{1}{2} \)[/tex] square centimeters.
First, convert the mixed fractions to improper fractions for easier multiplication:
[tex]\[ 22 \frac{1}{2} = 22 + \frac{1}{2} = \frac{44}{2} + \frac{1}{2} = \frac{45}{2} \][/tex]
[tex]\[ 562 \frac{1}{2} = 562 + \frac{1}{2} = \frac{1124}{2} + \frac{1}{2} = \frac{1125}{2} \][/tex]
Now, multiply these fractions to find the volume:
[tex]\[ \text{Volume} = \frac{45}{2} \times \frac{1125}{2} \][/tex]
[tex]\[ \text{Volume} = \frac{45 \times 1125}{2 \times 2} \][/tex]
[tex]\[ \text{Volume} = \frac{50625}{4} \][/tex]
Next, convert [tex]\( \frac{50625}{4} \)[/tex] to a mixed number by dividing:
[tex]\[ 50625 \div 4 = 12656.25 \][/tex]
Thus, the volume of the rectangular prism is:
[tex]\[ 12656.25 \, \text{cm}^3 = 12,656 \frac{1}{4} \, \text{cm}^3 \][/tex]
So, the correct answer is:
D. [tex]\( 12,656 \frac{1}{4} \, \text{cm}^3 \)[/tex]
