Question

calculate the volume of a square-based pyramid with an altitude height of 6 ft and base edges of 8 ft.
a $64\\ ft^3$
b $384\\ ft^3$
c $128\\ ft^3$
d $192\\ ft^3$

Explanation:

Step1: Calculate base area

The base is a square with side length $8$ ft. The area of a square is side length squared:
$A = 8^2 = 64$ $\text{ft}^2$

Step2: Apply pyramid volume formula

The volume $V$ of a pyramid is $\frac{1}{3} \times \text{base area} \times \text{height}$. Substitute base area $64$ $\text{ft}^2$ and height $6$ ft:
$V = \frac{1}{3} \times 64 \times 6$

Step3: Compute final volume

Simplify the expression:
$V = \frac{1}{3} \times 384 = 128$ $\text{ft}^3$

Answer:

C. 128 $ft^3$