Final answer:
The width of the base of the rectangular pyramid is 6 inches, which is found by rearranging and simplifying the formula for the volume of a pyramid using the given values for the pyramid's volume, height, and length.
Step-by-step explanation:
The student has asked about finding the width of the base of a rectangular pyramid with a known volume, height, and base length. To find the width (w), we use the formula for the volume of a pyramid: V = (1/3) × base area × height. The base area is the product of the base length (l) and width (w), so we can rewrite the equation as V = (1/3) × l × w × h, where
- V is the volume of the pyramid,
- l is the length of the base,
- w is the width of the base,
- h is the height of the pyramid.
Given that V = 1512 in³, h = 12 in, and l = 21 in, the equation becomes 1512 = (1/3) × 21 × w × 12. Simplifying, we find w = 1512 / (1/3 × 21 × 12), which calculates to 6 in. Hence, the width of the base of the pyramid is 6 inches.