The problem asks to find the volume of a rectangular pyramid. The given dimensions are: length = $9$ yd, width = $8$ yd, and height = $5$ yd. We need to find the volume and include the correct unit in the answer.

GeometryVolumePyramidsRectangular Pyramid3D Geometry
2025/4/16

1. Problem Description

The problem asks to find the volume of a rectangular pyramid. The given dimensions are: length = 99 yd, width = 88 yd, and height = 55 yd. We need to find the volume and include the correct unit in the answer.

2. Solution Steps

The formula for the volume of a pyramid is:
V=13BhV = \frac{1}{3}Bh
where VV is the volume, BB is the area of the base, and hh is the height of the pyramid.
Since the base is a rectangle, the area of the base is:
B=lwB = lw
where ll is the length and ww is the width.
In this case, l=9l = 9 yd and w=8w = 8 yd. So, the area of the base is:
B=(9 yd)(8 yd)=72 yd2B = (9 \text{ yd})(8 \text{ yd}) = 72 \text{ yd}^2
The height of the pyramid is given as h=5h = 5 yd. Now, we can calculate the volume of the pyramid:
V=13Bh=13(72 yd2)(5 yd)=13(360 yd3)=120 yd3V = \frac{1}{3}Bh = \frac{1}{3}(72 \text{ yd}^2)(5 \text{ yd}) = \frac{1}{3}(360 \text{ yd}^3) = 120 \text{ yd}^3

3. Final Answer

The volume of the rectangular pyramid is 120 yd3120 \text{ yd}^3.

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