Questions: Find the volume of a rectangular pyramid with a length of 14 in ., a width of 8 in ., and a height of 24 in. Round your answer to the nearest thousandth, if necessary.

Solution Steps

The volume \( V \) of a rectangular pyramid can be calculated using the formula: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

The base of the pyramid is a rectangle with a length of 14 inches and a width of 8 inches. The area \( A \) of the base is: \[ A = \text{Length} \times \text{Width} = 14 \, \text{in} \times 8 \, \text{in} = 112 \, \text{in}^2 \]

Using the height of 24 inches and the base area calculated in Step 2, the volume \( V \) is: \[ V = \frac{1}{3} \times 112 \, \text{in}^2 \times 24 \, \text{in} \] \[ V = \frac{1}{3} \times 2688 \, \text{in}^3 \] \[ V = 896 \, \text{in}^3 \]

Final Answer