Final answer:
To find the height of a rectangular prism with a volume of 585 cubic centimeters, length of 9 centimeters, and width of 13 centimeters, divide the volume by the product of the length and the width. The height (H) is 5 cm, so the correct answer is B. 5 cm.
Step-by-step explanation:
The volume of a rectangular prism is calculated by multiplying its length (L), width (W), and height (H). The formula is V = L × W × H. To find the height (H), when you know the volume and the other dimensions, you can rearrange the formula to H = V / (L × W). Given that the volume (V) is 585 cm³, the length (L) is 9 cm, and the width (W) is 13 cm, we can calculate the height by dividing the volume by the product of the length and width.
H = 585 cm³ / (9 cm × 13 cm)
H = 585 cm³ / 117 cm²
Therefore, H = 5 cm, which means the correct answer is B. 5 cm.