Question

try again
the value in your answer is incorrect.
find the volume of this rectangular pyramid.
be sure to include the correct unit in your answer.
(an image of a rectangular pyramid with base length 7 ft, base width 4 ft, and height 8 ft, along with an answer box and unit options ft, ft², ft³)

Explanation:

Step1: Recall the formula for the volume of a rectangular pyramid

The volume \( V \) of a rectangular pyramid is given by the formula \( V=\frac{1}{3} \times \text{length} \times \text{width} \times \text{height} \).

Step2: Identify the length, width, and height from the diagram

From the diagram, the length of the base is \( 7\,\text{ft} \), the width of the base is \( 4\,\text{ft} \), and the height of the pyramid is \( 8\,\text{ft} \).

Step3: Substitute the values into the formula

Substitute \( l = 7 \), \( w=4 \), and \( h = 8 \) into the formula:

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Wait, let's recalculate: \( 7\times4 = 28 \), \( 28\times8=224 \), then \( \frac{1}{3}\times224=\frac{224}{3}\approx74.67 \). But let's check the formula again. The volume of a pyramid is \( \frac{1}{3}Bh \), where \( B \) is the area of the base. The base is a rectangle with area \( B = length\times width=7\times4 = 28\,\text{ft}^2 \), and height \( h = 8\,\text{ft} \). Then \( V=\frac{1}{3}\times28\times8=\frac{224}{3}\approx74.67\,\text{ft}^3 \).

Answer:

\(\frac{224}{3}\) cubic feet (or approximately \( 74.67\,\text{ft}^3 \))