Question

find the volume of this rectangular pyramid. be sure to include the correct unit in your answer. image of rectangular pyramid with base length 7 in, base width 4 in, height 6 in input box unit options: in, in², in³ undo and clear buttons

Explanation:

Step1: Recall Volume Formula

The volume \( V \) of a rectangular pyramid is given by \( V = \frac{1}{3} \times \text{base area} \times \text{height} \). The base is a rectangle with length \( l = 7 \) in and width \( w = 4 \) in, and the height \( h = 6 \) in.

Step2: Calculate Base Area

The area of the rectangular base \( B \) is \( B = l \times w \). Substituting \( l = 7 \) and \( w = 4 \), we get \( B = 7 \times 4 = 28 \) \( \text{in}^2 \).

Step3: Substitute into Volume Formula

Now substitute \( B = 28 \) and \( h = 6 \) into the volume formula: \( V = \frac{1}{3} \times 28 \times 6 \). First, calculate \( 28 \times 6 = 168 \), then \( \frac{1}{3} \times 168 = 56 \).

Answer:

\( 56 \) cubic inches (or \( 56 \text{ in}^3 \))