The length of the base of the rectangular pyramid is approximately 3.43 inches.
Formula: We need the formula for the volume of a pyramid. It is:
Volume (V) = (1/3) * Base Area (A) * Height (h)
Given Information: We know the volume (V) is 56 in³, the height (h) is 7 inches, and the base width (w) is 7 inches.
Unknown: We need to find the length (l) of the base.
Solving for Base Area: We can rearrange the formula to solve for the base area (A):
A = (3 * V) / h
Substitute the known values:
A = (3 * 56 in³) / 7 in
A = 24 in²
Calculating Length: The base area is the product of the length and width:
A = l * w
We know the width (w) is 7 inches and the area (A) is 24 in². Substitute and solve for the length:
l = A / w
l = 24 in² / 7 in
l = 3.43 inches (approx.)
Therefore, the length of the base of the rectangular pyramid is approximately 3.43 inches.
Complete ques:
A rectangular pyramid has a volume of 56 in.³ if the height of the pyramid is 7 inches the width of the base what is the length of the base of the rectangle as base width is 7 inch?